Exploring Number Theory Concepts

What is the prime factorization of 84?

• 2 × 3 × 14

• 3 × 4 × 7

• 2^2 × 3 × 7

• 2^3 × 3 × 5

Find the greatest common divisor (GCD) of 48 and 180.

• 12

• 30

• 6

• 24

Calculate the least common multiple (LCM) of 12 and 15.

• 30

• 45

• 60

• 75

Using divisibility rules, is 12345 divisible by 3?

• Yes

• Yes, but only if it's a multiple of 5

• Yes, but only if it's even

• No

What are the integer properties of even numbers?

• Even numbers cannot be negative integers.

• Even numbers are integers that end with the digit 1.

• Even numbers are integers that are divisible by 2.

• Even numbers are always positive integers.

Determine the prime factorization of 60.

• 2^3 × 5

• 3 × 4 × 5

• 2 × 3 × 10

• 2^2 × 3 × 5

What is the GCD of 56 and 98?

• 7

• 49

• 14

• 28

Find the LCM of 8, 12, and 16.

• 24

• 64

• 48

• 36

Is 100 divisible by 5? Explain your answer.

• No, 100 is not a multiple of 5.

• No, because 100 is an even number.

• Yes, but only if it ends in 0.

• Yes

List the first five prime numbers.

• [2, 3, 5, 7, 11]

• 1, 4, 6, 8, 9

• 2, 4, 6, 8, 10

• 3, 5, 6, 8, 10