Question

complete the following.
(a) find the greatest common factor (gcf) of 32 and 12.
gcf =
(b) use the gcf to factor 32 - 12.
32 - 12 = × ( - )

Explanation:

Step1: Find GCF of 32 and 12

Factorize 32: \(32 = 2\times16 = 2\times2\times8 = 2\times2\times2\times4 = 2\times2\times2\times2\times2\)
Factorize 12: \(12 = 2\times6 = 2\times2\times3\)
Common factors: \(2\times2 = 4\)

Step2: Factor 32 - 12 using GCF

Divide 32 and 12 by GCF (4):
\(32\div4 = 8\), \(12\div4 = 3\)
So, \(32 - 12 = 4\times(8 - 3)\)

Answer:

(a) \(4\)
(b) \(4\times(8 - 3)\) (i.e., first box \(4\), second \(8\), third \(3\))