Step by step
The question
Question: find the greatest common factor of 28 and 42.
GCF(28, 42) = ?
A common factor goes into both numbers.
The greatest common factor, the GCF, is the biggest one.
common factor: goes into both
GCF: the greatest one
1 Find the prime factors
28 is even, so 2 goes in.
28 is 2 times 14.
28 = 2 × 14
14 is even, so 2 goes in.
14 is 2 times 7.
7 is prime, so we stop.
= 2 × 2 × 7
42 is even, so 2 goes in.
42 is 2 times 21.
42 = 2 × 21
3 goes into 21.
21 is 3 times 7.
7 is prime, so we stop.
= 2 × 3 × 7
2 Multiply the shared primes
Both have a 2.
Both have a 7.
We multiply the shared primes.
GCF(28, 42) = 2 × 7
2 times 7 is 14.
2 × 7 = 14
So the GCF is 14.
= 14
Careful: the GCF goes into every number.
So it is never bigger than the smallest one.
Careful: GCF ≤ the smallest number
3 Check
Let's check: 14 goes into each number.
28 ÷ 14 = 2
42 ÷ 14 = 3
No numbers are left over.
So 14 is right!
Let's look back.
First: find the prime factors.
Then: multiply the shared primes.
Last: check.
Answer
= 14