Question 1

Note: This is a knowledge of number theory question. Do not use a calculator for this question.
Select any choice that is a factor of 80,000,000,005,332.
3 4 5 6 8 9 12 15

Accepted Answer

The answer of Note: This is a knowledge of number...

Question 2

For each part, give an example, if one exists. If there is no example, explain why not.
A) A whole number that has 15, 21, and 1000 as factors but does not have 9 as a factor
B) A prime number that has 7 and 19 as factors and is not a perfect square

Accepted Answer

The answer of For each part, give an example, if...

Question 3

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Select each of the given choices that is a factor of the given number n. n = 2^{2 .} 10³^. 7^{11 .} 13⁵ $\text { Choices: } 8 \quad 14 \quad 21 \quad 28 \quad 35$

Accepted Answer

The answer of Note: This is a knowledge of number...

Question 4

If it is possible, give a whole number that is relatively prime to 24. If it is not possible, explain why.

Accepted Answer

The answer of If it is possible, give a whole...

Question 5

State a divisibility test for 4, and explain why it works.

Accepted Answer

The answer of State a divisibility test for 4, and...

Question 6

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Is it possible for some choice of positive whole numbers m and n that 75^m = 25ⁿ? Justify your decision.

Accepted Answer

The answer of Note: This is a knowledge of number...

Question 7

Write the prime factorization of the following. (Show your work.)
A) 1485
B) 792
C) Name all common factors of 1485 and 792. (They can be in factored form.)
D) What is the greatest common prime factor of 1485 and 792?

Accepted Answer

The answer of Write the prime factorization of the following....

Question 8

A) What is the least common multiple of 1485 and 792 (in factored form)?
B) Write two other common multiples of 1485 and 792.

Accepted Answer

The answer of A) What is the least common multiple...

Question 9

Suppose K = $2 ^ { 5 } \cdot 7 \cdot 11$ , L = $2 ^ { 3 } \cdot 7 \cdot 11 \cdot 13$ , M = $2 \cdot 29 ^ { 2 }$ , and N = $4 \cdot 11 \cdot 13 ^ { 2 } \cdot 29$ .
Name the least common multiple of each of the following (in factored form). 
A) K and L
B) M and N
C) K and M
D) K, L, and N

Accepted Answer

The answer of Suppose K = \(2 ^ { 5...

Question 10

Suppose K = $2 ^ { 5 } \cdot 7 \cdot 11$ , L = $2 ^ { 3 } \cdot 7 \cdot 11 \cdot 13$ , M = $2 \cdot 29 ^ { 2 }$ , and N = $4 \cdot 11 \cdot 13 ^ { 2 } \cdot 29$ 
. Name the greatest common factor of each of the following (in factored form). 
A) K and N
B) K and L
C) M and N
D) K, L, and M

Accepted Answer

The answer of Suppose K = \(2 ^ { 5...

Question 11

Write these numbers in simplest form.
A) $\frac { 26 } { 65 }$

B) $\frac { 616 } { 792 }$

C) $\frac { 129 } { 215 }$

Accepted Answer

The answer of Write these numbers in simplest form.
A) \(\frac...

Question 12

A) Use the prime factorizations of 345, 264, and 495 to find the least common multiple of the three numbers.
B) Compute the following: $\frac { 345 } { 495 } + \frac { 250 } { 264 }$  . (Leave the answer in factored form.)

Accepted Answer

The answer of A) Use the prime factorizations of 345,...

Question 13

Two neighboring satellites send out signals at regular intervals. One sends a signal every 180 seconds, and the other sends a signal every 280 seconds. If both satellites send out a signal at 12:00 midnight on January 1, when will be the next time that they both send out a signal at the same time?

Accepted Answer

The answer of Two neighboring satellites send out signals at...

Question 14

Hamburger patties come in packages of 16, and hamburger buns come in bags of 12. How many of each do you need to buy so that you have the same number of buns as you do hamburgers?

Accepted Answer

The answer of Hamburger patties come in packages of 16,...

Question 15

As a charitable service, your class undertakes a project where they fill backpacks with donated school supplies for underprivileged children. The donations include 135 notebooks, 216 pencils, and 81 pens. You want to use all the donations and include the same number of each item in each backpack. What is the largest number of backpacks you can fill, and how many items will be in each backpack?

Accepted Answer

The answer of As a charitable service, your class undertakes...

Question 16

Two football players are working out by running around a track. The first can run the track in 3 minutes, and the second one can run the track in 4 minutes. If they begin at the starting point at the same time and run in the same direction at the same rates, when will they both be at the starting point again?

Accepted Answer

The answer of Two football players are working out by...

Question 17

A band has been invited to march at the Rose Parade and needs to make money to cover the expenses. They divide up into three teams and shovel snow from long driveways for four days before Christmas. The first team makes $315, the second $240, and the third $210. If they charged the same whole-dollar rate for each driveway, what was that rate? Explain.

Accepted Answer

The answer of A band has been invited to march...

Quiz 11: Number Theory

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Select any choice that is a factor of 80,000,000,005,332. 3 4 5 6 8 9 12 15

For each part, give an example, if one exists. If there is no example, explain why not. A) A whole number that has 15, 21, and 1000 as factors but does not have 9 as a factor B) A prime number that has 7 and 19 as factors and is not a perfect square

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Select each of the given choices that is a factor of the given number n. n = 22 . 103 . 711 . 135 Choices: 814212835\text { Choices: } 8 \quad 14 \quad 21 \quad 28 \quad 35 Choices: 814212835

If it is possible, give a whole number that is relatively prime to 24. If it is not possible, explain why.

State a divisibility test for 4, and explain why it works.

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Is it possible for some choice of positive whole numbers m and n that 75m = 25n? Justify your decision.

Write the prime factorization of the following. (Show your work.) A) 1485 B) 792 C) Name all common factors of 1485 and 792. (They can be in factored form.) D) What is the greatest common prime factor of 1485 and 792?

A) What is the least common multiple of 1485 and 792 (in factored form)? B) Write two other common multiples of 1485 and 792.

Write these numbers in simplest form. A) 2665\frac { 26 } { 65 }6526​ B) 616792\frac { 616 } { 792 }792616​ C) 129215\frac { 129 } { 215 }215129​

A) Use the prime factorizations of 345, 264, and 495 to find the least common multiple of the three numbers. B) Compute the following: 345495+250264\frac { 345 } { 495 } + \frac { 250 } { 264 }495345​+264250​ . (Leave the answer in factored form.)

Two neighboring satellites send out signals at regular intervals. One sends a signal every 180 seconds, and the other sends a signal every 280 seconds. If both satellites send out a signal at 12:00 midnight on January 1, when will be the next time that they both send out a signal at the same time?

Hamburger patties come in packages of 16, and hamburger buns come in bags of 12. How many of each do you need to buy so that you have the same number of buns as you do hamburgers?

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Select each of the given choices that is a factor of the given number n. n = 2^{2 .} 10³^. 7^{11 .} 13⁵ $\text { Choices: } 8 \quad 14 \quad 21 \quad 28 \quad 35$

Note: This is a knowledge of number theory question. Do not use a calculator for this question. Is it possible for some choice of positive whole numbers m and n that 75^m = 25ⁿ? Justify your decision.

Write these numbers in simplest form. A) $\frac { 26 } { 65 }$ B) $\frac { 616 } { 792 }$ C) $\frac { 129 } { 215 }$

A) Use the prime factorizations of 345, 264, and 495 to find the least common multiple of the three numbers. B) Compute the following: $\frac { 345 } { 495 } + \frac { 250 } { 264 }$ . (Leave the answer in factored form.)