When a number is expressed as a product of its factors we say that the number has been factorised. When the factorization contains the prime number only then it is called prime factorization.Now let us look on how to find the prime factorization of 100

There are two method which can be used.

**Division method**

We divide the number 100 by 2, 3, 5, 7 etc. in this order repeatedly so long

as the quotient is divisible by that number.Thus, the prime factorization of 100 is $2 \times 2 \times 5 \times 5$

**Factor Tree Method**

In this method, we first think about any two factor and then we think about two factors of respective number. This goes till the factors are prime.

We may have different factor tree depending on the starting point but all of them will show the same prime factors.

Lets check the different Factor tree for 100

a. Starting with factor (2, 50)

Prime Factors are the Leaf Nodes. So , prime factorization of 100 is $2 \times 2 \times 5 \times 5$

b. starting with factor (20,5)

Prime Factors are the Leaf Nodes. So , prime factorization of 100 is $2 \times 2 \times 5 \times 5$

Prime Factors are the Leaf Nodes. So , prime factorization of 100 is $2 \times 2 \times 5 \times 5$

c. starting with factor (10,10)

Prime Factors are the Leaf Nodes. So , prime factorization of 100 is $2 \times 2 \times 5 \times 5$

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Table of Factors

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