Math Guide

Easy Ways to Learn Factoring

Introduction to factoring large numbers:

  • Letus study about the factoring large numbers. Factoring is defined as themethod which is used to get all the possible factors of a number.
  • Thistype of factoring method is also possible for large numbers. The large numbers under factoring method will get all their possible factors that may be prime ones or non prime ones.
  • Some of the examples for factoring large numbers are discussed in detail as below.

Factoring Large Numbers:

Factoring large numbers – example 1:

  • Do factoring for the large number 2160 using non prime or prime factorization method?

Solution:

  • First the number 2160 is factorized using the prime number 2 as 2160 is seemed to be as the occurrence of 1080 times of 2.
  • Nextdo factorization for the resulted number 1080 by another prime number 3as 1080 is seemed to be as the occurrence of 360 times of 3.
  • Thendo factoring with the next resulted number 360 by the same prime number3 as 360 is seemed to be as the occurrence of 120 times of 3.
  • Againthe factoring method is continued with the next resulted number 120 by non prime number 4 as 120 is seemed to be as the occurrence of 30 times of 4.
  • Continuing the factoring method with the next resulted number 30 by a prime number 5 as30 is seemed to be as the occurrence of 6 times of 5.
  • Therefore the final factors that are found for the given number 2160 are 2 x 3 x 3 x 4 x 5 x 6.

 

Factoring large numbers – example 2:

  • Do factoring for the large number 10080 using non prime or prime factorization method?

 

Solution:

  • First the number 10080 is factorized using the prime number 2 as 10080 is seemed to be as the occurrence of 5040 times of 2.
  • Nextdo factorization for the resulted number 5040 by another prime number 2as 5040 is seemed to be as the occurrence of 2520 times of 2.
  • Thendo factoring with the next resulted number 2520 by the non prime number8 as 2520 is seemed to be as the occurrence of 315 times of 8.
  • Againthe factoring method is continued with the next resulted number 315  byprime number 7 as 315  is seemed to be as the occurrence of 45 times of7.
  • Continuing the factoring method with the next resulted number 45 by a non prime number 9as 45 is seemed to be as the occurrence of 5 times of 9.
  • Therefore the final factors that are found for the given number 10080 are 2 x 2 x 8 x 7x 9 x 5.

 

Factoring large numbers – exercises:

  • Do factoring for the large number 5040 using non prime or prime factorization method? (Answer: 2 x 3 x 4 x 5 x 6 x 7)
  • Do factoring for the large number 5040 using non prime or prime factorization method? (Answer: 2 x 5 x 7 x 9 x 11 x 13)