Question

use the prime factors of the numbers in each set to calculate the greatest common factor.
a) 64 = 2 × 2 × 2 × 2 × 2 × 2
72 = 2 × 2 × 2 × 3 × 3
gcf = 2 × 2 × 2 = 8
b) 96
48
c) 20
8
d) 36
90
e) 60
44
f) 12
56
g) 28
8
h) 90
9
i) 72
96
j) 72
66

Explanation:

Part b)

Step1: Prime factorize 96

$96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3$

Step2: Prime factorize 48

$48 = 2 \times 2 \times 2 \times 2 \times 3$

Step3: Identify common prime factors

Common prime factors: $2^4 \times 3$ (but we take the minimum exponent for each common prime)
For 2: minimum exponent is 4 (from 48, since 48 has 4 2s and 96 has 5 2s)
For 3: minimum exponent is 1

Step4: Calculate GCF

$GCF = 2^4 \times 3 = 16 \times 3 = 48$

Step1: Prime factorize 20

$20 = 2 \times 2 \times 5$

Step2: Prime factorize 8

$8 = 2 \times 2 \times 2$

Step3: Identify common prime factors

Common prime factors: $2^2$ (minimum exponent of 2 is 2)

Step4: Calculate GCF

$GCF = 2^2 = 4$

Step1: Prime factorize 36

$36 = 2 \times 2 \times 3 \times 3$

Step2: Prime factorize 90

$90 = 2 \times 3 \times 3 \times 5$

Step3: Identify common prime factors

Common prime factors: $2^1 \times 3^2$ (minimum exponent of 2 is 1, minimum exponent of 3 is 2)

Step4: Calculate GCF

$GCF = 2 \times 3^2 = 2 \times 9 = 18$

Answer:

48

Part c)