Question

Find the common factors of 8, 20.

Answer 1

Hint: Here we have to find the common factors of 8 and 20. For that, we will find all the prime factors of the given two numbers by breaking the numbers into its smaller factors one by one, which is actually the prime factorization method. We will break all the numbers into prime factors by dividing first with the smallest prime number and then with the next prime number if it is not divisible by the first, we will continue this process until we will get all the factors as prime numbers. After getting the factors, we will check how many factors of the two given numbers are common and we will multiply all those factors to get the common factors of 8, 20.

Complete step-by-step answer:
Let’s find all the factors of 8.
As 8 is divisible by 2, so we can write 8 as $2\times 4$ i.e.
$8=2\times 4$
Now, we will break 4 into smaller factors. 4 is also divisible by 2. So we can write 4 as $2\times 2$
Thus,
$8=2\times 2\times 2$
Now, we can’t break any of the factors further. So the prime factorization of 8 is $2\times 2\times 2$.
Now, we will find all the factors of 20.
As 20 is exactly divisible by 2, so we can write 20 as $2\times 10$i.e.
$20=2\times 10$
Now, we will break 10 into smaller factors. 10 is also divisible by 2, so we can write 10 as
Thus,
$20=2\times 2\times 5$
Now, we can see that two factors are common between them which is $2\times 2$
Therefore, the common factor between 8 and 20 is 4.

Note: Since we have used the prime factorization method, we need to understand it properly.
A prime factorization method is the method of splitting the numbers into its smallest possible prime factors which when multiplied gives the original number.
Remember, all the factors which we get in the prime factorization method are prime numbers and not composite numbers.