Factors of 40: Prime Factors & Factor Pairs of 40

Factors of 40 are those numbers that divide the number 40 and result in a whole number as the quotient. The numbers that divide 40 completely leaving zero as the remainder are the factors of 40. 40 is a composite number which means that it has more than 2 factors. 1, 2, 4, 5, 8, 10, 20, and 40 are eight factors of 40. When we multiply two factors of a number in pairs and that results in the value of the original number, then, that set of numbers is called the pair factor. The pair factors of 40 are (1, 40), (2, 20), (4, 10), and (5, 8). The pair factors of 40 can be positive as well as negative. The prime factorization of 40 is 2 x 2 x 2 x 5. 

Key Terms: Factors of 40, Composite Number, Pair Factors, Prime Factors, Prime Factorization, Natural Numbers, Division, Remainder

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What are the Factors of 40?

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The number 40 is an even composite number which means that it will have more than 2 factors. Factors of 40 are the numbers that divide 40 exactly without leaving a remainder. In other words, the numbers when multiplied in pairs result in an original number are called the factors of 40. 

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

Factor Tree of 40

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How to Calculate Factors of 40?

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Factors of 40 can be calculated in a similar manner as other composite numbers. There are two main methods to calculate the factors of 40 which are:

1. Factors of 40 by Division Method
2. Factors of 40 by Prime Factorization

Both the division method and prime factorization would result in the same set of factors which are 1, 2, 4, 5, 8, 10, 20, and 40.

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Factors of 40 by Division Method

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In the division method, we will divide 40 by different consecutive integers. If the integer divides 40 completely without leaving any remainder, then, that integer is a factor of 40, else not. We will start dividing 40 by all the numbers starting from 1:

• 40/1 = 40 (Factor 1; Remainder 0)
• 40/2 = 20 (Factor 2; Remainder 0)
• 40/4 = 10 ( Factor 4; Remainder 0)
• 40/5 = 8 (Factor 5; Remainder 0)
• 40/8 = 5 (Factor 8; Remainder 0)
• 40/10 = 4 (Factor 10; Remainder 0)
• 40/20 = 2 (Factor 20; Remainder 0)
• 40/40 = 1 (Factor 40; Remainder 0)

We can see that 1, 2, 4, 5, 8, 10, 20 and 40 divide 40 completely thus, they are the factors of 40. Any other number apart from these numbers would result in a remainder. 

Read More: Multiplication and Division of Integers

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Prime Factorization of 40

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40 is a composite number that has prime factors. Here is a step-by-step procedure for the prime factorization of 40.

Prime Factorization of 40

• Divide the number 40 by the smallest prime factor which is 2. 40 ÷ 2 = 20
• Now divide 20 by 2, 20 ÷ 2 = 10.

• Now, keep on dividing unless you get an odd number. An odd number is not divisible by 2 and gives a fraction. So, we cannot consider a fraction as a factor. 10 ÷ 2 = 5
• If we divide 5 by 2 we will get a fraction number, so we will proceed to the next prime numbers, i.e. 3, 5, 7, and so on.

• Dividing 5 by 5 we get, 5 ÷ 5 = 1.

• 1 is received at the end and we cannot proceed with the division. 

The prime factorization of 40 is thus written as 2 × 2 × 2 × 5 or 23 × 5. 2 and 5 are the prime numbers which mean that they are the prime factors of 40.

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Pair Factors of 40

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Pair factors of 40 are the numbers that when multiplied together result in an original number of 40. We know that the pair factors of 40 can be positive or negative as if we multiply the pair of negative numbers, it will give the original number 40 only. The positive and negative pair factors of 40 are as follows:

Positive Pair Factors of 40

The positive pair factors of 40 are four which are (1, 40), (2, 20), (4, 10), and (5, 8).

Negative Pair Factors of 40

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

Solved Examples on Factors of 40

Example 1: What are the common factors of 40 and 41?

Solution: The factors of 40 and 41 are:

• Factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
• Factors of 41 are 1 and 41.

The common factor of 40 and 41 is only 1.

Example 2: List the common factors of 40 and 80.

Solution: Writing down all the factors of 40 and 80, we get

• Factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
• Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

The common factors of 40 and 80 are 1, 2, 4, 5, 8, 10, 20, and 40.

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Things to Remember

• Factors of 40 are the natural numbers that divide 40 completely.
• The factors of 40 leave zero as the remainder when on divisions with 40.
• There are total 8 factors of 40.
• 1, 2, 4, 5, 8, 10, 20, and 40 are the factors of 40.
• The pair factors of 40 are (1, 40), (2, 20), (4, 10), and (5, 8).
• The prime factorization of 40 is 2 × 2 × 2 × 5 or 2³ × 5.
• 2 and 5 are the two prime factors of 40.