Factor - Definition with Examples

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What is a Factors?

Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.  

Factors

 

Example:  3 × 5 = 15 therefore, 3 and 5 are the factors of 15.

This also means:

A factor divides a number completely without leaving any remainder.

Factors of Numbers

 

For example:  30 ÷ 6 = 5, and there is no remainder. So we can say that 5 and 6 are the factors of 30.

In the given example, we can further break up or simplify the number 6 into its factors, that is, 2 and 3. In other words, when we multiply 5, 2 and 3, we still get 30. Therefore, the factors of 30 are 5, 2, and 3. Also, 5 × 2 = 10. So, 10 is also a factor of 30. Similarly, 5 × 3 = 15. So, 15 is also a factor of 30. Finally, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

  • The number 1 is the smallest factor of every number.

  • Every number will have a minimum of two factors, 1 and the number itself.

  • A number that has only two factors, 1 and the number itself, is called a prime number.

 

Prime factorization

  • When we write a number as a product of all its prime factors, it is called prime factorization.

  • Every number in prime factorization is a prime number.

  • Sometimes to write the prime factors of a number we might have to repeat a number.

 Prime factorization
 

  Fun Facts

  • Factors are always whole numbers or integers and never decimals or fractions.

  • All even numbers will have number 2 as their factor.

  • All numbers that end with 5 will have 5 as their factor.

  • All numbers greater than 0 and ending with a 0 will have 2, 5, and 10 as their factors.

  • Algebraic expressions are often solved or simplified through factoring.

 

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