When we explore the factors of a number, we are looking for all the numbers that can divide it exactly without leaving any remainder. Factors are like the building blocks of a number. They are important for many math problems and help us understand the properties of the number better. We'll dive into the factors of **74**, understand how to calculate them, and learn about some related concepts.

## What Are Factors?

Factors are numbers that you can multiply together to get another number. For example, when we think about the number **74**, we want to find all the pairs of whole numbers that can be multiplied to get **74**. These pairs are the factors of **74**.

## List of Factors of 74

Here are the factors of **74**:

- 1
- 2
- 37
- 74

## How to Calculate Factors of 74

Calculating the factors of **74** involves finding all the numbers that can divide **74** without leaving a remainder. This can be done using two methods: the multiplication method and the division method.

## Factors of 74 Using the Multiplication Method

In the multiplication method, we look for pairs of numbers that, when multiplied together, equal **74**.

- Start with the number
**1**(since 1 is a factor of every number). - Now, we pair it with
**74**: 1 multiplied by 74 equals 74. - Next, we check
**2**: 2 multiplied by 37 equals 74.

We see that beyond these pairs, any other pairs either repeat the same factors or don't multiply to 74. So, the pairs we found are:

1 and 74

2 and 37

## Factors of 74 Using the Division Method

The division method involves dividing **74** by different numbers to see which divisions result in a whole number.

**74 / 1 = 74**(whole number, so 1 is a factor).**74 / 2 = 37**(whole number, so 2 is a factor).**74 / 37 = 2**(whole number, so 37 is a factor).**74 / 74 = 1**(whole number, so 74 is a factor).

These divisions confirm that the factors of **74** are 1, 2, 37, and 74.

## What Is Prime Factorization?

Prime factorization is breaking down a number into the set of prime numbers which, when multiplied together, give the original number. A **prime number** is a number greater than 1 that has no positive divisors other than 1 and itself.

## Prime Factors of 74

Here are the prime factors of **74**:

- 2
- 37

## Conclusion

Understanding factors is crucial in math because they reveal the building blocks of numbers. We found that the factors of **74** are 1, 2, 37, and 74, and its prime factors are 2 and 37. Knowing how to calculate these helps in many areas like simplifying fractions, finding greatest common divisors, and more.

## FAQs

**Q: What are factors?**

A: Factors are numbers that divide another number exactly without leaving a remainder.

**Q: What are the prime factors of 74?**

A: The prime factors of 74 are 2 and 37.

**Q: How do we use the multiplication method to find factors?**

A: We find pairs of numbers that, when multiplied together, give the original number.

**Q: How do we use the division method to find factors?**

A: We divide the number by possible factors and check which divisions result in whole numbers.