Introduction to Factoring With Numbers

This lesson is designed to explore decomposition, multiplication, and factoring of whole numbers and the distributive property.

Problem 1:

Factor out a common factor of 5 from 45.

Step 1:

The expanded form of 45 is written as follows

45 = 40 + 5

Step 2:

The common factor of 5 and 40 is 5 itself.

Step 3:

Using distributive property to factor out the common factor 5

45 = (40 + 5) = (5 × 8 + 5 × 1) = 5(8 + 1)

Problem 2:

Given a number 36

(i) Factor out a common factor of 2

(ii) Factor out a common factor of 6

Step 1:

The expanded form of given number is written as follows

36 = 30 + 6

Step 2:

Using distributive property

(i) Factoring out a common factor of 2

36 = 30 + 6 = 2 × 15 + 2 × 3 = 2(15 + 3)

Step 3:

Using distributive property

(ii) Factoring out a common factor of 6

36 = 30 + 6 = 5 × 6 + 1 × 6 = 6(5 + 1)