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Factors and Products

Multiplication involves at least two numbers. The two numbers are multiplied together to give the product. The numbers multiplied are called the factors of the product number.
Example: 4 x 5 is 20.Factors are numbers being multiplied.

In a multiplication problem, the numbers that are multiplied are called as factors and multiplying these factors is called as product. Factor means taking a number way from the product. The reverse of multiplication is called as factor. For example: Multiplying 4 and 2 we get 8 as a product. Here 4 and 2 is called as two factors. It can be divided into two division facts: 8 ÷ 2 = 4, and 8 ÷ 4 = 2. So, 8 are divisible by both 4 and 2. The factors of 8 are 4 and 2.

Numerical factors are numbers used as factors.
Example: Here, 20 is the product and 4, 5 are the factors of 20. 4 and 5 exactly divides 20.


Literal factors
are alphabets or letters being used in place of or represent numbers used for multiplication.
Example: (m) (n) = 24; here, 'm' and 'n' are literal factors.Interchanging the factors do not change the product value ( commutative law of multiplication).
Interchanging of factors may be used to
(a) simplify the multiplication
(b) re-arrange the factors in a preferred order
(c) check the product value

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Factors and Products Rules

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There are some rules for factors and products.

  • Finding factor is a method of breaking down the number into smaller ones.
  • The factor of a number exactly divides that number.
  • All factors of a number are less than or equal to the number.
  • Each number is a factor of itself.
  • 1 is a factor of all numbers.

Thus, a product is the multiple of all its factors. These are some of the properties of factors and products.

Divisibility Rules

Divisibility rules help to find the factors of a number. Finding factors of a number means, we start dividing the number to get exact divisors.

  • Products are opposites of factors.
  • Products of a number are obtained by multiplying that number with other numbers.
  • 20 is the product of 5 with 4. 25 is the product of 5 with 5.
  • Product of a number is always greater than or equal to the number. 20 > 5.

Every number is the product of itself and 1.

Factors and Products Examples

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Given below are some of the examples on factors and products.

Solved Examples

Question 1: Find the factors of 60.
Solution:
 
Applying divisibility test, 60 is divisible by 10

60 = 6 x 10

60 = 3 x 2 x 2 x 5

Factors of 60 are 1, 2, 3, 5, 60.
 

Question 2: Find the factors of 24
Solution:
 

Factor rainbows are a method of listing the factors of a number and the factor pairs that multiply to give the number are joined by curves.

Factors of 24 = 1 x 24 = 2 x 12 = 4 x 6= 8 x 3

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

Factors and Products


 

Question 3: Find the factors of 120
Solution:
 

Factor tree is another method of representing factors.

120 = 12 x 10 = 4 x 3 x 2 x 5 = 2 x 2 x 3 x 2 x 5

We break down 120 to simple factors using the divisibility test. Then, each factor is broken down to more simple numbers.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60,120.

Factors and Products Rules


 

More topics in Factors and Products
Divisibility Test
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