Mastering Factors and Fractions

Find the prime factors of 60.

• 2, 3, 5

• 2, 2, 3, 5

• 3, 5, 7

• 2, 3, 7

Answer explanation

To find the prime factors of 60, we can divide it by the smallest prime numbers. 60 = 2 x 30, 30 = 2 x 15, 15 = 3 x 5. Thus, the prime factors are 2, 2, 3, and 5, making the correct choice 2, 2, 3, 5.

Calculate the greatest common factor (GCF) of 48 and 64.

• 8

• 12

• 16

• 24

Answer explanation

To find the GCF of 48 and 64, we can list the factors: 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and 64 (1, 2, 4, 8, 16, 32, 64). The largest common factor is 16, making it the GCF.

Calculate the least common multiple (LCM) of 6 and 8.

• 24

• 30

• 36

• 48

Answer explanation

To find the LCM of 6 and 8, list the multiples: 6 (6, 12, 18, 24...) and 8 (8, 16, 24...). The smallest common multiple is 24, making it the LCM. Thus, the correct answer is 24.

Answer explanation

To rename \( \frac{3}{4} \) with a denominator of 16, multiply both the numerator and denominator by 4: \( \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \). Thus, the correct answer is \( \frac{12}{16} \).

Tags

CCSS.3.NF.A.3B

CCSS.4.NF.A.1

• Cannot be determined

Answer explanation

To compare \(\frac{5}{8}\) and \(\frac{3}{4}\), convert \(\frac{3}{4}\) to eighths: \(\frac{3}{4} = \frac{6}{8}\). Since \(\frac{5}{8} < \frac{6}{8}\), it follows that \(\frac{5}{8} < \frac{3}{4}\).

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

Answer explanation

To simplify \( \frac{18}{24} \), find the greatest common divisor (GCD) of 18 and 24, which is 6. Divide both the numerator and denominator by 6: \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \). Thus, the correct answer is \( \frac{3}{4} \).

Find the prime factors of 84.

• 2, 3, 7

• 2, 2, 3, 7

• 3, 5, 7

• 2, 3, 5

Answer explanation

To find the prime factors of 84, we can divide it by the smallest prime number, 2, repeatedly: 84 ÷ 2 = 42, 42 ÷ 2 = 21, then 21 ÷ 3 = 7. Thus, the prime factors are 2, 2, 3, and 7.

Calculate the greatest common factor (GCF) of 36 and 54.

• 6

• 9

• 12

• 18

Answer explanation

To find the GCF of 36 and 54, we can list the factors: 36 (1, 2, 3, 4, 6, 9, 12, 18, 36) and 54 (1, 2, 3, 6, 9, 18, 27, 54). The largest common factor is 18, making it the GCF.

Calculate the least common multiple (LCM) of 5 and 7.

• 30

• 35

• 40

• 45

Answer explanation

To find the LCM of 5 and 7, we multiply them since they are both prime: 5 x 7 = 35. Thus, the least common multiple of 5 and 7 is 35.

Answer explanation

To rename \( \frac{2}{5} \) with a denominator of 20, multiply both the numerator and denominator by 4: \( \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \). Thus, the correct answer is \( \frac{8}{20} \).

Tags

CCSS.3.NF.A.3B

CCSS.4.NF.A.1