Question

Using division method, find the prime factor of 150075

Answer 1

In prime factorization, we factorize the numbers into prime numbers, called prime factors.

There are two methods of prime factorization:

1. Division Method

2. Factor Tree Method


Prime Factorization by Division Method

Observe the following steps.

I: First we divide the number by the smallest prime number which divides the number exactly.

II: We divide the quotient again by the smallest or the next smallest prime number if it is not exactly divisible by the smallest prime number. We repeat the process again and again till the quotient becomes 1. Remember, we use only prime numbers to divide.

III: We multiply all the prime factors. Remember, the product is the number itself.

Let us consider a few examples using division method.

1. Find the prime factors of 15.

First Step: 2 is the smallest prime number. But it cannot divide 15 exactly. So, consider 3.

Second Step: Now, 5 cannot be divide by 3. Consider the next smallest prime number 5.

The prime factors of 15 are 3 × 5.


2. Find the prime factors of 18.

First Step: Consider 2, the smallest prime number.

Second Step: As 9 cannot be divide by 2. Consider the next smallest prime 3. Repeat the process till quotient becomes 1.

The prime factors of 18 are 2 × 3 × 3.