Find Prime Factorization/Factors Of 40 - Cuemath

Explore factors using illustrations and interactive examples.

• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
• Factors of 15 - The factors of 15 are 1, 3, 5, 15
• Factors of 140 - The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
• Factors of 400 - The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Factors of 40 by Prime Factorization

Prime factorization means expressing a composite number as the product of its prime factors. To get the prime factorization of 40, we divide it by its smallest prime factor, which is 2, 40 ÷ 2 = 20. Now, 20 is divided by its smallest prime factor and the quotient is obtained. This process goes on till we get the quotient as 1.

The prime factorization of 40 is shown below:

Factors Pair Factor 1 × 40 = 40 (1,40) 2 × 20= 40 (2,20) 4 × 10 = 40 (4,10) 5 × 8 = 40 (5,8) 8 × 5 = 40 (8,5) 10 × 4 = 40 (10,4) 20 × 2 = 40 (20,2) 40 × 1 = 40 (40,1)

• Observe in the table above, after 5 × 8, the factors start repeating. So, it is enough to find factors till (5,8)
• If we consider negative integers, then both the numbers in the pair factors will be negative. We know that - ve × - ve = +ve
• So, we can have factor pairs of 40 as (-1,-40) ; (-2,-20); (-4,-10); (-5,-8)

Challenging Questions:

• Are 0.4 and 100 factors of 40? Why do you think so?
• Are -5 and 8 factors of 40? Why do you think so?

 

Factors of 40 Solved Examples

1. Example 1: Peter and Andrew both have rectangular papers with dimensions as shown below.

   The length and breadth of the first rectangular paper are 8 inches and 5 inches, and the length and breadth of the second rectangular paper are 10 inches and 4 inches. They place the two rectangles one over another. Since the two shapes do not overlap, Peter said that they don't have the same area. However, Andrew does not agree with him. Can you find out who is correct?

   Solution: Area of a rectangle = length × breadth For the first rectangle, Area = 8 × 5 = 40 For the second rectangle, Area = 10 × 4 = 40 Hence, the two rectangles have equal areas and Andrew is correct.

2. Example 2: Jill has (-4) as one of the factors of 40. How will she get the other factor?

   Solution: 40 = Factor 1 × Factor 2, so we can say that 40 = (-4) × Factor 2. Now, calculating for factor 2, Factor 2 = 40 ÷ (-4) = (-10).

   Hence, the other factor is -10.

3. Example 3: Find the Least Common Multiple and Greatest Common Factor (GCF) of 40 and 36.

   Solution:

   The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 and factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Therefore, the Least Common Multiple of 40 and 36 is 360 and the Greatest Common Factor (GCF) of 40 and 36 is 4.

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FAQs on Factors of 40

What are the Factors of 40?

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 and its negative factors are -1, -2, -4, -5, -8, -10, -20, -40.

What are the Prime Factors of 40?

The prime factors of 40 are 2, 5.

What is the Sum of the Factors of 40?

Sum of all factors of 40 = (23 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) = 90

What is the Greatest Common Factor of 40 and 28?

The factors of 40 and 28 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 4, 7, 14, 28 respectively. Common factors of 40 and 28 are [1, 2, 4]. Hence, the Greatest Common Factor of 40 and 28 is 4.

How Many Factors of 40 are also Factors of 30?

Since, the factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 and the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. Hence, [1, 2, 5, 10] are the common factors of 40 and 30.