When we talk about factors in math, we're discussing numbers you can multiply together to get another number. For example, the factors of 90 are the numbers that, when multiplied in pairs, result in 90. Understanding factors is quite useful in various areas of math, from simplifying fractions to finding common denominators.

## What Are Factors of 90?

Factors of 90 are the numbers you can multiply in pairs to get 90. Factors are important because they help in breaking down complex problems into simpler parts. For the number 90, there are multiple pairs of factors that can make the product of 90.

## List of Factors of 90

- 1
- 10
- 18
- 2
- 3
- 30
- 45
- 5
- 6
- 9
- 90

## How to Calculate the Factors of 90

To figure out which numbers are factors of 90, we need to see which numbers can divide 90 without leaving a remainder. There are two main methods to do this: the multiplication method and the division method. Let's look at each method in more detail.

## Calculating Factors Using the Multiplication Method

The multiplication method involves finding pairs of numbers that multiply to make 90. To do this, start with the number 1 and work your way up:

- 1 * 90 = 90
- 2 * 45 = 90
- 3 * 30 = 90
- 5 * 18 = 90
- 6 * 15 = 90
- 9 * 10 = 90

Each of these pairs shows that both numbers are factors of 90. Notice how the list of pairs includes both smaller numbers like 1 and 3, and larger numbers like 90 and 30.

## Calculating Factors Using the Division Method

The division method involves dividing 90 by different numbers to see if the result is a whole number:

- 90 / 1 = 90
- 90 / 2 = 45
- 90 / 3 = 30
- 90 / 5 = 18
- 90 / 6 = 15
- 90 / 9 = 10
- 90 / 10 = 9
- 90 / 15 = 6
- 90 / 18 = 5
- 90 / 30 = 3
- 90 / 45 = 2
- 90 / 90 = 1

In each of these cases, both numbers involved in the division (the divisor and the quotient) are factors of 90. This method helps confirm if a number is a factor by checking for a remainder of zero.

## What is Prime Factorization?

Prime factorization is the process of breaking down a number into its prime factors. A prime number is a number that has no other factors besides 1 and itself. Prime factorization is useful for simplifying complex mathematical problems and finding greatest common divisors.

## Prime Factors of 90

- 2
- 3
- 5

The prime factorization of 90 is 2 * 3 * 3 * 5. When multiplied together, these prime numbers give you 90. Prime factorization helps us understand the building blocks of our number more deeply.

## Conclusion

In summary, the factors of 90 include several pairs of numbers that, when multiplied together, give 90. We can use either the multiplication or division method to find these factors. The prime factors of 90 are 2, 3, and 5, which help us break down the number into its simplest components. Understanding factors and prime factorization is not just useful in academic settings but also in practical applications like simplifying fractions and solving complex equations.

## FAQs

**Q1: What is the greatest factor of 90?**

The greatest factor of 90 is 90 itself.

**Q2: How many total factors does 90 have?**

The number 90 has a total of 12 factors.

**Q3: What are the prime numbers that are factors of 90?**

The prime numbers that are factors of 90 are 2, 3, and 5.

**Q4: Can 90 be divided by 7 without a remainder?**

No, 90 divided by 7 does not result in a whole number; it leaves a remainder.

**Q5: Is 45 a factor of 90?**

Yes, 45 is a factor of 90 because 45 times 2 equals 90.