What is prime factorization of 80

The factors of 80 are the numbers that divide 80 exactly without leaving any remainder.  The factors of 80 can be a positive or negative number. Similarly, the pair factors of 80 can also be represented in positive or negative form. For example, the pair factor of 80 can be represented as (1, 80) or (-1, -80). If we multiply a pair of negative numbers, such as multiplying -1 and -80, it will result in the original number 80. In this article, we are going to learn the factors of 80, pair factors and the prime factors of 80 using the prime factorization method and many solved examples.

Table of Contents:

What are the Factors of 80?

The factors of 80 are the numbers that divide 80 completely and leave a remainder 0. In other words, if we multiply a pair of numbers and it results in a product of the original number 80, then the numbers are the factors of 80. As 80 is an even composite number, the number 80 has many factors other than 1 and 80. Hence, the factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80. Similarly, the negative factors of 80 are -1, -2, -4, -5, -8, -10, -16, -20, -40 and -80.

Pair Factors of 80

The pair factor of 80 is a pair of numbers, which are multiplied together resulting in the original number 80. As discussed above, the pair factors of 80 can be positive or negative, but they cannot be a fraction or decimal. Thus, the positive and negative pair factors of 80 are given below:

Positive Pair Factors of 80:

Thus, the positive pair factors of 80 are (1, 80), (2, 40), (4, 20), (5, 16) and (8, 10).

Negative Pair Factors of 80:

Thus, the negative pair factors of 80 are (-1, -80), (-2, -40), (-4, -20), (-5, -16) and (-8, -10).

Factors of 80 by Division Method

In the division method, the factors of 80 are found by dividing 80 by different integer numbers. If the number divides 80 exactly and leaves the remainder 0, then those integers are the factors of 80. Now, let us discuss how to find the factors of 80 by division method.

• 80/1 = 80 (Factor is 1 and Remainder is 0)
• 80/2 = 40 (Factor is 2 and Remainder is 0)
• 80/4 = 20 (Factor is 4 and Remainder is 0)
• 80/5 = 16 (Factor is 5 and Remainder is 0)
• 80/8 = 10 (Factor is 8 and Remainder is 0)
• 80/10 = 8 (Factor is 10 and Remainder is 0)
• 80/16 = 5 (Factor is 16 and Remainder is 0)
• 80/20 = 4 (Factor is 20 and Remainder is 0)
• 80/40 = 2 (Factor is 40 and Remainder is 0)
• 80/80 = 1 (Factor is 80 and Remainder is 0)

If any numbers other than 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 divide 80, it leaves a remainder of some value. Hence, the factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

Prime Factorization of 80

In the prime factorization method, the number 80 is written as the product of the prime factors of 80. Now, let us discuss how to find the prime factors of 80 using the prime factorization method. 

Take the pair factor of 80, say (1, 80)

Here, leave the number 1, as it is neither prime nor composite.

Now, take the other factor 80. As we know, 80 is an even composite number and hence it can be factored into its prime factors.

80 is written as the product of 5 and 16.

Now, 5 is a prime number and 16 is a composite number.

In terms of prime factors, 16 is written as 2×2×2×2.

Now, write the number 80 in the form of a product of its prime factors.

Thus, 80 = 2×2×2×2×5

Hence, the prime factorization of 80 is 2×2×2×2×5 or 24×5.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 80 and 79.

Solution:

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

The factors of 79 are 1 and 79.

As 79 is a prime number, the common factor of 80 and 79 is 1.

Example 2:

Find the common factors of 80 and 81.

Solution:

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

Factors of 81 = 1, 3, 9, 27 and 81.

Hence, the common factor of 80 and 81 is 1.

Example 3:

Find the common factors of 80 and 40.

Solution:

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

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

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

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