The question
Question: find the factors of 12.
Factors of 12
A factor of 12 is a whole number that goes into 12 exactly.
Nothing is left over.
factor: goes into 12 exactly
1 Find the factor pairs
We start with 1.
1 goes into every number: 1 times 12 is 12.
Each number that goes in comes with a partner.
= 1 × 12 = 12
12 divided by 2 is 6.
Nothing is left over.
So 2 times 6 is 12.
= 2 × 6 = 12
12 divided by 3 is 4.
Nothing is left over.
So 3 times 4 is 12.
= 3 × 4 = 12
Next is 4.
But 4 times 4 is 16, more than 12.
From here the pairs only repeat.
So we stop.
4 × 4 = 16 > 12 → stop
2 List them in order
Now we write them from small to big.
First the orange numbers, going down.
Then the purple numbers, going up.
= 1, 2, 3, 4, 6, 12
So 12 has 6 factors: 1, 2, 3, 4, 6 and 12.
Let's look back.
First: find the factor pairs.
Last: list them in order.
Answer = 1, 2, 3, 4, 6, 12
▶ Watch it solved
The question
Question: find the factors of 100.
Factors of 100
A factor of 100 is a whole number that goes into 100 exactly.
Nothing is left over.
factor: goes into 100 exactly
1 Find the factor pairs
We start with 1.
1 goes into every number: 1 times 100 is 100.
Each number that goes in comes with a partner.
= 1 × 100 = 100
100 divided by 2 is 50.
Nothing is left over.
So 2 times 50 is 100.
= 2 × 50 = 100
Does 3 go in?
100 divided by 3 is 33, with 1 left over.
So 3 is not a factor.
= 100 ÷ 3 = 33 r 1 ✗
r 1 = 1 left over
100 divided by 4 is 25.
Nothing is left over.
So 4 times 25 is 100.
= 4 × 25 = 100
100 divided by 5 is 20.
Nothing is left over.
So 5 times 20 is 100.
= 5 × 20 = 100
Does 6 go in?
100 divided by 6 is 16, with 4 left over.
So 6 is not a factor.
= 100 ÷ 6 = 16 r 4 ✗
Does 7 go in?
100 divided by 7 is 14, with 2 left over.
So 7 is not a factor.
= 100 ÷ 7 = 14 r 2 ✗
Does 8 go in?
100 divided by 8 is 12, with 4 left over.
So 8 is not a factor.
= 100 ÷ 8 = 12 r 4 ✗
Does 9 go in?
100 divided by 9 is 11, with 1 left over.
So 9 is not a factor.
= 100 ÷ 9 = 11 r 1 ✗
100 divided by 10 is 10.
Nothing is left over.
So 10 times 10 is 100.
= 10 × 10 = 100
The pair meets: 10 times 10.
So we stop.
the pair meets → stop
2 List them in order
Now we write them from small to big.
First the orange numbers, going down.
Then the purple numbers, going up.
= 1, 2, 4, 5, 10, 20, 25, 50, 100
So 100 has 9 factors: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Let's look back.
First: find the factor pairs.
Last: list them in order.
Answer = 1, 2, 4, 5, 10, 20, 25, 50, 100
▶ Watch it solved
The question
Question: find the greatest common factor of 48 and 180.
GCF(48, 180) = ?
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
48 is even, so 2 goes in.
48 is 2 times 24.
48 = 2 × 24
24 is even, so 2 goes in.
24 is 2 times 12.
= 2 × 2 × 12
12 is even, so 2 goes in.
12 is 2 times 6.
= 2 × 2 × 2 × 6
6 is even, so 2 goes in.
6 is 2 times 3.
3 is prime, so we stop.
= 2 × 2 × 2 × 2 × 3
180 is even, so 2 goes in.
180 is 2 times 90.
180 = 2 × 90
90 is even, so 2 goes in.
90 is 2 times 45.
= 2 × 2 × 45
3 goes into 45.
45 is 3 times 15.
= 2 × 2 × 3 × 15
3 goes into 15.
15 is 3 times 5.
5 is prime, so we stop.
= 2 × 2 × 3 × 3 × 5
2 Multiply the shared primes
Both have a 2.
Both have another 2.
Both have a 3.
We multiply the shared primes.
GCF(48, 180) = 2 × 2 × 3
2 times 2 is 4.
4 times 3 is 12.
2 × 2 = 4
4 × 3 = 12
So the GCF is 12.
= 12
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: 12 goes into each number.
48 ÷ 12 = 4
180 ÷ 12 = 15
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.
▶ Watch it solved
