Factors and Multiples

What are the factor pairs of 36?

• (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)

• (1, 36), (2, 18), (3, 12), (4, 8), (6, 6)

• (1, 36), (2, 18), (3, 12), (5, 7), (6, 6)

• (1, 36), (2, 18), (3, 11), (4, 9), (6, 6)

Answer explanation

The factor pairs of 36 are combinations of two numbers that multiply to 36. The correct pairs are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). The other options contain incorrect pairs.

What is the prime factorization of 60?

Answer explanation

To find the prime factorization of 60, we divide it by the smallest prime numbers: 60 = 2 × 30, 30 = 2 × 15, 15 = 3 × 5. Thus, 60 = 2^2 × 3 × 5, making the correct choice 2^2 × 3 × 5.

Which of the following is the greatest perfect square that is a factor of 72?

• 4

• 9

• 16

• 36

Answer explanation

To find the greatest perfect square factor of 72, we first factor 72 into its prime factors: 72 = 2^3 * 3^2. The perfect squares from the factors are 1, 4 (2^2), 9 (3^2), and 36 (6^2). The greatest is 36.

What are the factor pairs of 45?

• (1, 45), (3, 15), (5, 9)

• (1, 45), (3, 14), (5, 9)

• (1, 45), (3, 15), (5, 8)

• (1, 45), (2, 22), (5, 9)

Answer explanation

The factor pairs of 45 are the pairs of numbers that multiply to give 45. The correct pairs are (1, 45), (3, 15), and (5, 9). Other options include incorrect pairs that do not multiply to 45.

What is the prime factorization of 84?

Answer explanation

To find the prime factorization of 84, we divide it by the smallest prime numbers: 84 = 2 × 42, 42 = 2 × 21, 21 = 3 × 7. Thus, 84 = 2^2 × 3 × 7, making the correct choice 2^2 × 3 × 7.

Which of the following is the greatest perfect square that is a factor of 50?

• 4

• 9

• 16

• 25

Answer explanation

The factors of 50 are 1, 2, 5, 10, 25, and 50. Among these, the perfect squares are 1 (1x1) and 25 (5x5). The greatest perfect square factor of 50 is 25.

What are the factor pairs of 28?

• (1, 28), (2, 14), (4, 7)

• (1, 28), (2, 13), (4, 7)

• (1, 28), (3, 14), (4, 7)

• (1, 28), (2, 14), (5, 7)

Answer explanation

The factor pairs of 28 are the pairs of numbers that multiply to give 28. The correct pairs are (1, 28), (2, 14), and (4, 7). Other options include incorrect pairs that do not multiply to 28.

What is the prime factorization of 90?

Answer explanation

To find the prime factorization of 90, we divide it by the smallest prime numbers: 90 = 2 × 45, then 45 = 3 × 15, and 15 = 3 × 5. Thus, the prime factorization is 2 × 3^2 × 5, which matches the correct choice.

Which of the following is the greatest perfect square that is a factor of 98?

• 4

• 9

• 16

• 49

Answer explanation

To find the greatest perfect square factor of 98, we factor 98 into 2 x 7 x 7. The perfect squares from the factors are 1, 4, and 49. Among these, 49 is the greatest perfect square that divides 98.

What are the factor pairs of 100?

• (1, 100), (2, 50), (4, 25), (5, 20), (10, 10)

• (1, 100), (2, 50), (4, 24), (5, 20), (10, 10)

• (1, 100), (3, 50), (4, 25), (5, 20), (10, 10)

• (1, 100), (2, 50), (4, 25), (5, 19), (10, 10)

Answer explanation

The correct factor pairs of 100 are (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10). Each pair multiplies to 100, confirming they are valid factors.