Question 1

Provide the appropriate response.
-Find the greatest 3-digit number that has exactly three factors.

Accepted Answer

A) 973 
B) 999 
C) 961 
D) 963 
A) 973 
B) 999 
C) 961 
D) 963

Question 2

Find the LCM for the given numbers by an appropriate method.
-45, 56, and 150

Accepted Answer

A) 1260 
B) 12,600 
C) 2520 
D) 1,050 
A) 1260 
B) 12,600 
C) 2520 
D) 1,050

Question 3

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 34,210 divisible by 10?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 4

Provide the appropriate response.
-Find the least number divisible by each natural number less than or equal to 10.

Accepted Answer

A) 30,240 
B) 3,628,800 
C) 2520 
D) 100 
A) 30,240 
B) 3,628,800 
C) 2520 
D) 100

Question 5

Find the GCD or LCM as indicated.
-Given 48, 162, and 9, find the LCM.

Accepted Answer

A) 648 
B) 324 
C) 432 
D) 1296 
A) 648 
B) 324 
C) 432 
D) 1296

Question 6

$$\operatorname { LCM } ( a , b ) \geq a$$

Accepted Answer

A) True 
 B)False

Question 7

Solve the problem.
-If all of 82 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Accepted Answer

A) No 
B) Yes, two. 
C) Yes, three. 
A) No 
B) Yes, two. 
C) Yes, three.

Question 8

Find the GCD or LCM as indicated.
-Given 8 and 28, find the LCM.

Accepted Answer

A) 28 
B) 224 
C) 14 
D) 56 
A) 28 
B) 224 
C) 14 
D) 56

Question 9

Without using a calculator, determine whether the first number is divisible by the second number.
-Is 732,275 divisible by 5?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 10

Provide the appropriate response.
-List all primes between 100 and 200 .

Accepted Answer

A)  $101,103,107,109,113,127,131,137,139,149,151,153,157,163,165,167,173,179,181,191$, 197, 199 
B)  $101,107,109,127,131,137,139,149,151,157,167,179,181,191,193,197,199$ 
C)  $101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197$, 199 
D)  $101,103,107,113,127,131,137,151,157,163,167,173,179,181,191,197$ 
A)  $101,103,107,109,113,127,131,137,139,149,151,153,157,163,165,167,173,179,181,191$, 197, 199 
B)  $101,107,109,127,131,137,139,149,151,157,167,179,181,191,193,197,199$ 
C)  $101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197$, 199 
D)  $101,103,107,113,127,131,137,151,157,163,167,173,179,181,191,197$

Question 11

Provide the appropriate response.
-There is a number that has 2, 5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?

Accepted Answer

A) 80 
B) 40 
C) 320 
D) 70 
A) 80 
B) 40 
C) 320 
D) 70

Question 12

Determine all possible digits to place in the square that make the statement true. If none exist, state this.
-$$214,21 \square \text { is divisible by } 11 \text {. }$$

Accepted Answer

The answer of Determine all possible digits to place in...

Question 13

Find the GCD or LCM as indicated.
-Given 240, 10,000, and 2250, find the GCD.

Accepted Answer

A) 20 
B) 30 
C) 50 
D) 10 
A) 20 
B) 30 
C) 50 
D) 10

Question 14

Find the GCD or LCM as indicated.
-Given 30 and 90, find the LCM.

Accepted Answer

A) 90 
B) 270 
C) 180 
D) 30 
A) 90 
B) 270 
C) 180 
D) 30

Question 15

Using divisibility tests, solve the problem.
-Aryana is organizing the seating for a banquet. Is it possible for her to sit 289 people at 12 different tables so that each table has the same number of people?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 16

Use least common multiple or greatest common divisor to solve the problem.
-Rob can complete his bus route in 6 hours. Joan can complete her bus route in 3 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the Next time they would leave the terminal at the same time.

Accepted Answer

A) 12:00 pm 
B) 9:00 am 
C) 6:00 am 
D) Not enough information given to tell 
A) 12:00 pm 
B) 9:00 am 
C) 6:00 am 
D) Not enough information given to tell

Question 17

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$
-$$\text { If } \mathrm { d } \nmid \mathrm { a } ^ { 2 } \text {, then } \mathrm { d } \nmid \mathrm { a } \text {. }$$

Accepted Answer

A) True 
 B)False

Question 18

If a number is divisible by 3 and 5, then it must also be divisible by 15.

Accepted Answer

A) True 
 B)False

Question 19

Use least common multiple or greatest common divisor to solve the problem.
-Mark has 153 hot dogs and 171 hamburgers. He wants to put the same number of hot dogs and hamburgers on each tray. What is the greatest number of trays Mark can use to accomplish this?

Accepted Answer

A) 51 
B) 3 
C) 9 
D) 323 
A) 51 
B) 3 
C) 9 
D) 323

Question 20

Find the GCD for the given numbers by an appropriate method.
-120, 1000, and 11,250

Accepted Answer

A) 20 
B) 30 
C) 50 
D) 10 
A) 20 
B) 30 
C) 50 
D) 10

Provide the appropriate response. -Find the greatest 3-digit number that has exactly three factors.

Find the LCM for the given numbers by an appropriate method. -45, 56, and 150

Without using a calculator, determine whether the first number is divisible by the second number. -Is 34,210 divisible by 10?

Provide the appropriate response. -Find the least number divisible by each natural number less than or equal to 10.

Find the GCD or LCM as indicated. -Given 48, 162, and 9, find the LCM.

$\operatorname { LCM } ( a , b ) \geq a$

Solve the problem. -If all of 82 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Find the GCD or LCM as indicated. -Given 8 and 28, find the LCM.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 732,275 divisible by 5?

Provide the appropriate response. -List all primes between 100 and 200 .

Provide the appropriate response. -There is a number that has 2, 5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $214,21 \square \text { is divisible by } 11 \text {. }$

Find the GCD or LCM as indicated. -Given 240, 10,000, and 2250, find the GCD.

Find the GCD or LCM as indicated. -Given 30 and 90, find the LCM.

Using divisibility tests, solve the problem. -Aryana is organizing the seating for a banquet. Is it possible for her to sit 289 people at 12 different tables so that each table has the same number of people?

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid \mathrm { a } ^ { 2 } \text {, then } \mathrm { d } \nmid \mathrm { a } \text {. }$

If a number is divisible by 3 and 5, then it must also be divisible by 15.

Use least common multiple or greatest common divisor to solve the problem. -Mark has 153 hot dogs and 171 hamburgers. He wants to put the same number of hot dogs and hamburgers on each tray. What is the greatest number of trays Mark can use to accomplish this?

Find the GCD for the given numbers by an appropriate method. -120, 1000, and 11,250

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 4: Number Theory

Provide the appropriate response. -Find the greatest 3-digit number that has exactly three factors.

Find the LCM for the given numbers by an appropriate method. -45, 56, and 150

Without using a calculator, determine whether the first number is divisible by the second number. -Is 34,210 divisible by 10?

Provide the appropriate response. -Find the least number divisible by each natural number less than or equal to 10.

Find the GCD or LCM as indicated. -Given 48, 162, and 9, find the LCM.

LCM⁡(a,b)≥a\operatorname { LCM } ( a , b ) \geq aLCM(a,b)≥a

Solve the problem. -If all of 82 available apple trees are to be planted on a plot of land, is there more than one possible array in which they can be arranged with the same number of trees in each row? If so, how many Different arrays are there?

Find the GCD or LCM as indicated. -Given 8 and 28, find the LCM.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 732,275 divisible by 5?

Provide the appropriate response. -List all primes between 100 and 200 .

Provide the appropriate response. -There is a number that has 2, 5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 214,21□ is divisible by 11. 214,21 \square \text { is divisible by } 11 \text {. }214,21□ is divisible by 11.

Find the GCD or LCM as indicated. -Given 240, 10,000, and 2250, find the GCD.

Find the GCD or LCM as indicated. -Given 30 and 90, find the LCM.

Using divisibility tests, solve the problem. -Aryana is organizing the seating for a banquet. Is it possible for her to sit 289 people at 12 different tables so that each table has the same number of people?

Classify as true or false, assuming that a, b, c, and d are whole numbers an d≠0\mathrm { d } \neq 0d=0 - If d∤a2, then d∤a. \text { If } \mathrm { d } \nmid \mathrm { a } ^ { 2 } \text {, then } \mathrm { d } \nmid \mathrm { a } \text {. } If d∤a2, then d∤a.

If a number is divisible by 3 and 5, then it must also be divisible by 15.

Use least common multiple or greatest common divisor to solve the problem. -Mark has 153 hot dogs and 171 hamburgers. He wants to put the same number of hot dogs and hamburgers on each tray. What is the greatest number of trays Mark can use to accomplish this?

Find the GCD for the given numbers by an appropriate method. -120, 1000, and 11,250

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

$\operatorname { LCM } ( a , b ) \geq a$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $214,21 \square \text { is divisible by } 11 \text {. }$

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid \mathrm { a } ^ { 2 } \text {, then } \mathrm { d } \nmid \mathrm { a } \text {. }$