Factors of 400 Using Prime Factorization
Factors of 400
We will be able to understand the factors of 400 through the following table that has the factors, factor pairs and the prime factors of 400.
What are the Factors of 400?
The factors of 400 are integers that divide 400 without leaving any remainder. In other words, the factors of 400 are the divisors of 400.
For example: 40 is a factor of 400 because when we divide 400 by 40, it gives us 10 as the quotient and 0 as the remainder. The quotient 10 is also a factor of 400.
So, to check if any number is a factor of 400, divide 400 by that number and check whether the remainder is zero or not.
Factor List of 400
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400
Prime Factorization of 400
The factor tree of 400 can be written as:
From the factor tree, we can see that the prime factorization of 400 is 2 × 2 × 2 × 2 × 5 × 5 = \(2^4\times5^2\).
This means 2 and 5 are prime factors of 400.
Factor Pairs of 400
The factor pair of 400 is the set of two factors of 400, that when multiplied together, result in 400.
The factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400
Example: (4, 100) is a factor pair of 400 as 4 and 100 are the factors of 400 and 4 \(\times\) 100 = 400.
Positive Factor Pairs of 400
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Rapid Recall
Solved Factors of 400 Examples
Example 1: Find the common factors of 400 and 100.
Solution:
The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
The factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.
So, the common factors of 400 and 100 are 1,2, 4, 5, 10, 20, 25, 50 and 100.
Example 2: How many factors does 400 have?
Solution:
The factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400
So, there are 15 factors of 400.
Example 3: Shane has 225 pencils and Jax has 400 pencils. Find the greatest common factor that can completely divide the number of pencils that Shane has and the number of pencils that Jax has.
Solution:
To find the greatest common factor, we will have to first find the common factors of 225 and 400.
The factors of 400 = 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.
The factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, and 225.
The common factors of 120 and 225 are 1, 5 and 25.
Therefore, the greatest common factor that can divide both 400 and 225 is 25.
No, because when we divide 400 by 17, we get 9 as a remainder, that is, 17 does not divide 400 exactly.
The numbers that divide 400 exactly, that is, leave zero as the remainder, are known as the factors of 400.
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.
Hence, the sum of all the factors of 400 is
= 1 + 2 + 4 + 5 + 8 + 1 0 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 200 + 400 = 961
Hence, the sum is 961.
Yes, 400 is a composite number as it has factors other than 1 and itself. It has the factors 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100 and 200 other than 1 and 400.
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.
So, the least factor of 400 is 1 and the greatest factor is 400 itself.