Factors of 400 | How to Find the Prime Factors of 400 by the Prime Factorization Method? (2024)

The factors of 400 are the numbers that divide 400 evenly and leave a remainder value of 0. The factors and the factor pairs of 400 can be represented in both positive and negative forms. For example, the pair factor of 400 can be represented as (1, 400) or (-1, -400). If we multiply a pair of negative numbers, such as multiplying -1 and -400, it will result in the original number. Thus, the factors of 400 can be positive or negative, but they cannot be a decimal or a fractional number. In this article, we are going to learn the factors of 400, positive and negative pair factors of 400, how to find the prime factors of 400 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 400?
• Pair Factors of 400
• Factors of 400 by Division Method
• Prime Factorization of 400
• Solved Examples
• FAQs

What are the Factors of 400?

The numbers that are multiplied together in pairs resulting in the original number 400 are the factors of 400. In other words, the numbers that divide 400 completely without leaving any remainder are the factors of 400. As the number 400 is an even composite number, it has many factors other than 1 and 400. Therefore, the factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400. Similarly, the negative factors of 400 are -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -200 and -400.

Pair Factors of 400

As discussed above, the pair factors of 400 can be in a positive or negative form. Since the number 400 is a composite number, it has more than one pair factor. The following are the positive and the negative pair factor of 400.

Positive Pair Factors of 400:

Therefore, the positive pair factors of 400 are (1, 400), (2, 200), (4, 100), (5, 80), (8, 50), (10, 40), (16, 25) and (20, 20).

Negative Pair Factors of 400:

Hence, the negative pair factors of 400 are (-1, -400), (-2, -200), (-4, -100), (-5, -80), (-8, -50), (-10, -40), (-16, -25) and (-20, -20).

Factors of 400 by Division Method

In the division method, the factors of 400 are easily found by dividing 400 by different integers. If the integer divides 400 evenly, then the integer is a factor of a number 400. Thus, the factors of 400 are found using the division method as follows.

Start dividing the number 400 by 1 and then continue with the different integers.

• 400/1 = 400 (Factor is 1 and Remainder is 0)
• 400/2 = 200 (Factor is 2 and Remainder is 0)
• 400/4 = 100 (Factor is 4 and Remainder is 0)
• 400/5 = 80 (Factor is 5 and Remainder is 0)
• 400/8 = 50 (Factor is 8 and Remainder is 0)
• 400/10 = 40 (Factor is 10 and Remainder is 0)
• 400/16 = 25 (Factor is 16 and Remainder is 0)
• 400/20 = 20 (Factor is 20 and Remainder is 0)
• 400/25 = 16 (Factor is 25 and Remainder is 0)
• 400/40 = 10 (Factor is 40 and Remainder is 0)
• 400/50 = 8 (Factor is 50 and Remainder is 0)
• 400/80 = 5 (Factor is 80 and Remainder is 0)
• 400/100 = 4 (Factor is 100 and Remainder is 0)
• 400/200 = 2 (Factor is 200 and Remainder is 0)
• 400/400 = 1 (Factor is 400 and Remainder is 0)

Thus, the factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

Note: If we divide 400 by any numbers other than 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400, it leaves a remainder of some integer value.

Prime Factorization of 400

In the prime factorization of 400, the number 400 is written as the product of its prime factors. Thus, the process to find the prime factors of 400 using the prime factorization method are as follows:

Take a pair factor of 400, say (1, 400). Here, the number 400 is an even composite number, which can be further divided into its prime factors.

We can write the number 400 as the product of 20 and 20, but still, 20 is a composite number.

So, again split the number 20 into its prime factors.

(i.e) 400 = 20 × 20

Split the number 20 into its prime factors.

20 = 4 × 5 = 2 × 2 × 5

20 = 4 × 5 = 2 × 2 × 5, where 2 and 5 are the prime numbers.

Thus, 400 is written as 2 × 2 × 2 × 2 × 5 × 5.

Therefore, the prime factorization of 400 is 2 × 2 × 2 × 2 × 5 × 5 or 2⁴ × 5².

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 400 and 397.

Solution:

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

The factors of 397 are 1 and 397.

As the number 397 is a prime number, the common factor of 400 and 397 is 1.

Example 2:

What are the common factors of 400 and 401?

Solution:

Factors of 400 = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

Factors of 401 = 1 and 401.

Hence, the common factor of 400 and 401 is 1.

Example 3:

Find the common factors of 400 and 200.

Solution:

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.

Therefore, the common factors of 400 and 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.

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