Question

How do you find all the factors of 147?

Answer 1

Hint:Here we will use the prime factorization method to find the factors of the given number. For that, we will first divide the given number by the least prime number and then again we will divide the obtained number by the next least possible prime number. We will repeat the process until we get the prime number after division. From there, we will get all the factors of the given number.

Complete step by step solution:
 Here we need to find all the factors of the given number and the given number is 147.
We will use the prime factorization method to find the factors of the given number.
Now, we will first divide the given number i.e. 147 by the least prime factor 3.
\[{\rm{147}} \div 3 = 49\]
Again we will divide the obtained number by the next least prime factor 7.
\[49 \div 7 = 7\]
As we can see that the 7 is a prime number. So we can’t factorize that number further.

Therefore, the prime factors of the given number i.e. 147 are equal to \[3 \times 7 \times 7\].

Note: Factors of a number are defined as the numbers which when multiplied together gives the original numbers. So when we multiply factors 3, 7, and 7 together, we will get the number 147. We need to keep in mind that if a number is odd then all the factors of this odd number will also be odd and none of its factors will be even. Here, we have taken the least prime number as 3 and not 2 because the given number is an odd number and it is not completely divisible by 2.