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Multiples, factors and prime factors

Multiples, factors and prime factors

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Explainer Video

Tutor: Alice

Summary

Multiples, factors and prime factors

​​In a nutshell

Every number is either a prime number, or a multiple of other factors.



Multiples, factors and primes

  • Multiple - A multiple of a number is any number that can be formed as a product of that number and another number.
  • Factor - A factor of a number is any number that divides the number with no remainder.
  • Prime number - A prime number is a number which has only two distinct factors, 111 and itself.​


Example 1

What are the factors of 363636?

36=1×3636 = 1 \times 3636=1×36

36=2×1836 = 2 \times 1836=2×18​​​

36=3×1236 = 3 \times 1236=3×12

36=4×936 = 4 \times 936=4×9​​​

36=6×636 = 6\times 636=6×6


Hence the factors of 363636 are 1,2,3,4,6,9,12,18,36‾\underline{1,2,3,4,6,9,12,18,36}1,2,3,4,6,9,12,18,36​.


Example 2

Is 162162162 a multiple of 272727?

162÷27=6162 \div 27 = 6162÷27=6


Yes, 162162162 is a multiple of 272727, as the quotient (666) is a whole number and there is no remainder.



Factor trees

You can find the prime factorisation of a number using a factor tree.


Procedure

  1. ​Write the number at the top and find two numbers which multiply to make the number.
  2. Write the pair of factors underneath the original number, "branching" them off to the left and right of the original number.
  3. If one, or both, of these factors are not prime, repeat this process until the end of every "branch" is a prime number.
  4. Write the numbers at the bottom of each branch, multiplied by one another. This is the prime factorisation.


Example 3

Use a factor tree to find the prime factorisation of 273273273.


​    273  ↙↘3◯ 91 ↙↘    7◯ 13◯\quad\quad\quad\space{\begin{aligned} &\space \space \,\,273\\\ &\,\,\swarrow\searrow& \\&\textcircled{3}\,\,\,\,\, \quad91 \\&\quad\,\,\swarrow\searrow\\&\space\space\space\,\,\textcircled7 \,\,\,\,\quad\textcircled{13} \\\end{aligned}}  ​  273↙↘3◯91↙↘   7◯13◯​​​


Hence the prime factorisation of 273273273 is 273=3×7×13‾\underline{273 = 3 \times 7 \times 13}273=3×7×13​.


Note: If the original number is, itself, a prime number then you already have the number in its prime factorisation form.


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FAQs - Frequently Asked Questions

Can a factor of a number be greater than the number?

The factor of a number is always less than or equal to the given number.

Can a number have multiple prime factorisations?

No, a number having two distinct factorisations into primes is impossible.

What is the difference between multiples, factors and prime factors?

A prime is a number that has only two factors which are 1 and itself. A multiple is a number in the given number's times table. A factor is a number that fits into another number exactly.

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