Step by step
The question
Question: find the greatest common factor of 24, 36 and 60.
A common factor goes into all the numbers.
The greatest common factor, the GCF, is the biggest one.
1 Find the prime factors
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.
36 is even, so 2 goes in.
36 is 2 times 18.
18 is even, so 2 goes in.
18 is 2 times 9.
3 goes into 9.
9 is 3 times 3.
3 is prime, so we stop.
60 is even, so 2 goes in.
60 is 2 times 30.
30 is even, so 2 goes in.
30 is 2 times 15.
3 goes into 15.
15 is 3 times 5.
5 is prime, so we stop.
2 Multiply the shared primes
All three have a 2.
All three have another 2.
All three 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.