# Prime Factorization Tree

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Prime factorization tree method is one of the useful methods for prime factorization. The product of all the prime factors for the number gives back the original number. Prime factorization of a given number is expressing the given number as a product of all prime numbers. Prime number is a number which has no other factors other than one and itself.

Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29……..

Example: Find the prime factorization of the number 204?

Solution: Divide the given number with the smallest prime number.

204 ÷ 2 = 102; 204 = 2 * 102

Now 102 is further divided by 2.

102 ÷ 2 = 51; 102 = 2 * 51.

Now 51 can be divided by the prime number 3.

51 = 3 * 17; 51 = 3 * 17.

Now the number 17 is a prime number which cannot be further divided by any other number other that one and itself.

Hence 204 = 2 *2 * 3 * 17.

Example: Find the prime factorization of the number 220?

Solution: Divide the given number with the smallest prime number.

220 ÷ 2 = 110; 220 = 2 * 110

Now 110 is further divided by 2.

110 ÷ 2 = 55; 110 = 2 * 55.

Now 55 can be divided by the prime number 5.

55 = 5* 11;

Now the number 11 is a prime number which cannot be further divided by any other number other that one and itself.

Hence 220 = 2 *2 * 5 * 11.