# Factors of 74

Factors of 74 are 1, 2, 37, and 74

#### How to find factors of a number

 1.   Find factors of 74 using Division Method 2.   Find factors of 74 using Prime Factorization 3.   Find factors of 74 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 74

• Divide 74 by 1: 74 ÷ 1 : Remainder = 0
• Divide 74 by 2: 74 ÷ 2 : Remainder = 0
• Divide 74 by 37: 74 ÷ 37 : Remainder = 0
• Divide 74 by 74: 74 ÷ 74 : Remainder = 0

Hence, Factors of 74 are 1, 2, 37, and 74

#### 2. Steps to find factors of 74 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 74 using the division method, follow these steps:

• Step 1. Start dividing 74 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 74, which is 2. Divide 74 by 2 to obtain the quotient (37).
74 ÷ 2 = 37
• Step 3. Repeat step 1 with the obtained quotient (37).
37 ÷ 37 = 1

So, the prime factorization of 74 is, 74 = 2 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 74 as shown below:

So, the prime factorization of 74 is, 74 = 2 x 37.

#### 3. Find factors of 74 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 74 would be the two numbers which, when multiplied, give 74 as the result.

The following table represents the calculation of factors of 74 in pairs:

Factor Pair Pair Factorization
1 and 74 1 x 74 = 74
2 and 37 2 x 37 = 74

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 74. They are called negative pair factors.

Hence, the negative pairs of 74 would be ( -1 , -74 ) , ( -2 , -37 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 74 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 37, 74 are exact divisors of 74.
• 1 is a factor of every number. Eg. 1 is a factor of 74.
• Every number is a factor of zero (0), since 74 x 0 = 0.

• What two numbers make 74?

Two numbers that make 74 are 2 and 37.

• What is prime factorization of 74?

Prime factorization of 74 is 2 x 37.

• Write some multiples of 74?

First five multiples of 74 are 148, 222, 296, 370.

• Which is the smallest prime factor of 74?

The smallest prime factor of 74 is 2.

• Is 74 a perfect square?

No 74 is not a perfect square.

• What is the sum of all factors of 74?

The sum of all factors of 74 is 114.

• What are factors of 74?

Factors of 74 are 1, 2, 37, 74.

• How do you find factors of a negative number? ( eg. -74 )?

Factors of -74 are -1, -2, -37, -74.

• Is 74 a whole number?

Yes 74 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 74. Help him in finding the mean of 74.

Factors of 74 are 1, 2, 37, 74.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 74 is 1 + 2 + 37 + 74 = 114.
Hence, the mean of factors of 74 is 114 ÷ 4 = 28.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 74? Help her in writing all the factors.

Positive factors are 1, 2, 37, 74.
Negative factors are -1, -2, -37, -74.

Joey wants to write all the prime factors of 74 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 74 are 2, 37.
So in exponential form it can be written as 2 x 37.

Kevin has been asked to write 3 factor(s) of 74. Can you predict the answer?

3 factor(s) of 74 are 1, 2, 37.

Sammy is puzzled while calculating the prime factors of 74. Can you help him find them?

Factors of 74 are 1, 2, 37, 74.
Prime factors of 74 are 2, 37

What is prime factorization of 74?

Prime factorization of 74 is 2 x 37 = 2 x 37.

Can you help Rubel to find out the product of the even factors of 74?

Factors of 74 are 1, 2, 37, 74.
Even factors of 74 are 2, 74.
Hence, product of even factors of 74 is; 2 x 74 = 148.