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# What are all the factors, the prime factorization, and factor pairs of 100?

To find the factors of 100, divide 100 by each number starting with 1 and working up to 100

Now let us find how to calculate all the factors of 100:
2
= 50
4
= 25
5
= 20
10
= 10
As you can see, the factors of 100 are:
1, 2, 4, 5, 10, 20, 25, 50, 100

## Introduction to Factors

Factors are the building blocks of numbers, the whole numbers that are multiplied together to produce a given product. With 100 as our example, we can unravel the multipliers that unite to form 100. Understanding these factors illuminates the broader significance of 100 within mathematics, presenting a clearer view of its fundamental structure and properties.

## What are Factors of 100?

The factors of 100 are numbers that divide 100 without leaving any remainder. When these factors are paired and multiplied, they yield the product 100. Below is a visual representation of these factors and their corresponding pairs.

• 1 × 100
• 2 × 50
• 4 × 25
• 5 × 20
• 10 × 10

The list of factors for 100 is extensive, simplifying our understanding of how multiplication undergirds the composition of 100.

## How to Find the Factors of 100?

Discovering the factors of 100 via division is straightforward. Factors are numbers less than or equal to 100 that, when divided into 100, result in a whole number. Here is a breakdown of this process:

Consider number 1; every number is divisible by 1:

100 ÷ 1 = 100

Now, since 100 is equal to 10 squared, it is also divisible by 10:

100 ÷ 10 = 10

This systematic division continues with smaller divisors that are factors of 100:

• 100 ÷ 2 = 50
• 100 ÷ 4 = 25
• 100 ÷ 5 = 20
• …(and so on until we cover all factors).

If a number other than a factor divides 100, the result will not be whole, signifying it’s not a factor.

For instance, 100 ÷ 3 = 33.333, which is not a whole number.

## Pair Factors of 100

Pair factors of 100 are essentially numerical partners that multiply to give 100. Such factors occur in both positive and negative polarity without altering the product’s positivity. Below is the list of such pairs:

Positive Pair Factors Negative Pair Factors
(1, 100) (-1, -100)
(2, 50) (-2, -50)
(4, 25) (-4, -25)
(5, 20) (-5, -20)
(10, 10) (-10, -10)

## Prime Factorization of 100

Delving into the prime factorization of 100 involves breaking it down into its prime constituents. A prime factor is a prime number that divides 100 without leaving any remainder. By creating a factor tree, we simplify 100 into its prime factors. Follow the steps illustrated in the factor tree diagram below:

• 100 → 2 × 50
• 50 → 2 × 25
• 25 → 5 × 5
• Resulting prime factorization: 2 × 2 × 5 × 5 or 2² × 5²

## Important Points to Remember

Key takeaways about the factors of 100 include:

• Total factors: 9
• Prime factors: 2, 5
• Pair factors: (1, 100), (2, 50), (4, 25), (5, 20), (10, 10)
• Sum of factors: 1+2+4+5+10+20+25+50+100 = 217

It’s particularly notable that 100 is a perfect square, and the symmetry of its factors is echoed in its square root, 10.

## Exercises

Try to answer these questions to test your understanding of the factors of 100:

1. What is the highest even factor of 100?
2. How many factors of 100 are also multiples of 10?

## Solutions to Exercises

Here are the answers to the exercises:

• The highest even factor of 100 is 100 itself.
• There are 5 factors of 100 that are also multiples of 10: 10, 20, 50, and 100.

### What are the Factors of 100?

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

### How Many Factors of 100 are Prime?

There are two prime factors of 100: 2 and 5.

### Is 10 a Factor of 100?

Yes, 10 is a factor of 100.