Step by step
The question
Question: find the greatest common factor of 48 and 180.
A common factor goes into both numbers.
The greatest common factor, the GCF, is the biggest one.
1 Find the prime factors
48 is even, so 2 goes in.
48 is 2 times 24.
24 is even, so 2 goes in.
24 is 2 times 12.
12 is even, so 2 goes in.
12 is 2 times 6.
6 is even, so 2 goes in.
6 is 2 times 3.
3 is prime, so we stop.
180 is even, so 2 goes in.
180 is 2 times 90.
90 is even, so 2 goes in.
90 is 2 times 45.
3 goes into 45.
45 is 3 times 15.
3 goes into 15.
15 is 3 times 5.
5 is prime, so we stop.
2 Multiply the shared primes
Both have a 2.
Both have another 2.
Both have a 3.
We multiply the shared primes.
2 times 2 is 4.
4 times 3 is 12.
So the GCF is 12.
Careful: the GCF goes into every number.
So it is never bigger than the smallest one.
3 Check
Let's check: 12 goes into each number.
No numbers are left over.
So 12 is right!
Let's look back.
First: find the prime factors.
Then: multiply the shared primes.
Last: check.