Question

1. determine the greatest common factor of each set of numbers.

a) 40, 48, 56
b) 84, 120, 144

Explanation:

Step1: Prime factorize 40, 48, 56

$40 = 2^3 \times 5$, $48 = 2^4 \times 3$, $56 = 2^3 \times 7$

Step2: Find shared prime factors

The lowest power of shared prime 2 is $2^3$

Step3: Calculate GCF for part a

$2^3 = 8$

Step4: Prime factorize 84, 120, 144

$84 = 2^2 \times 3 \times 7$, $120 = 2^3 \times 3 \times 5$, $144 = 2^4 \times 3^2$

Step5: Find shared prime factors

Lowest powers of shared primes: $2^2$, $3^1$

Step6: Calculate GCF for part b

$2^2 \times 3 = 4 \times 3 = 12$

Answer:

a) 8
b) 12