# Factors of 76

Factors of 76 are 1, 2, 4, 19, 38, and 76

#### How to find factors of a number

 1.   Find factors of 76 using Division Method 2.   Find factors of 76 using Prime Factorization 3.   Find factors of 76 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 76

• Divide 76 by 1: 76 ÷ 1 : Remainder = 0
• Divide 76 by 2: 76 ÷ 2 : Remainder = 0
• Divide 76 by 4: 76 ÷ 4 : Remainder = 0
• Divide 76 by 19: 76 ÷ 19 : Remainder = 0
• Divide 76 by 38: 76 ÷ 38 : Remainder = 0
• Divide 76 by 76: 76 ÷ 76 : Remainder = 0

Hence, Factors of 76 are 1, 2, 4, 19, 38, and 76

#### 2. Steps to find factors of 76 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 76 using the division method, follow these steps:

• Step 1. Start dividing 76 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 76, which is 2. Divide 76 by 2 to obtain the quotient (38).
76 ÷ 2 = 38
• Step 3. Repeat step 1 with the obtained quotient (38).
38 ÷ 2 = 19
19 ÷ 19 = 1

So, the prime factorization of 76 is, 76 = 2 x 2 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 76 as shown below:

So, the prime factorization of 76 is, 76 = 2 x 2 x 19.

#### 3. Find factors of 76 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 76 would be the two numbers which, when multiplied, give 76 as the result.

The following table represents the calculation of factors of 76 in pairs:

Factor Pair Pair Factorization
1 and 76 1 x 76 = 76
2 and 38 2 x 38 = 76
4 and 19 4 x 19 = 76

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 76. They are called negative pair factors.

Hence, the negative pairs of 76 would be ( -1 , -76 ) , ( -2 , -38 ) and ( -4 , -19 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 76 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 76.
• Every number is a factor of zero (0), since 76 x 0 = 0.
• 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, 4, 19, 38, 76 are exact divisors of 76.
• Factors of 76 are 1, 2, 4, 19, 38, 76. Each factor divides 76 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 19, 38, 76 are all less than or equal to 76.

• Is 76 a perfect square?

No 76 is not a perfect square.

• What are factors of 76?

Factors of 76 are 1, 2, 4, 19, 38, 76.

• Which is greatest factor of 76?

The greatest factor of 76 is 38.

• What is the sum of all factors of 76?

The sum of all factors of 76 is 140.

• What are multiples of 76?

First five multiples of 76 are 152, 228, 304, 380.

• What is the greatest prime factors of 76?

The greatest prime factor of 76 is 19.

• What are six multiples of 76?

First five multiples of 76 are 152, 228, 304, 380, 456, 532.

• What is prime factorization of 76?

Prime factorization of 76 is 2 x 2 x 19.

• Is 76 a whole number?

Yes 76 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 76? Help her in writing all the factors.

Positive factors are 1, 2, 4, 19, 38, 76.
Negative factors are -1, -2, -4, -19, -38, -76.

Can you help Sammy find out the product of the odd factors of 76?

Factors of 76 are 1, 2, 4, 19, 38, 76.
Odd factors of 76 are 1, 19.
Hence product of odd factors of 76 is; 1 x 19 = 19.

Joey wants to write all the prime factors of 76 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 76 are 2, 2, 19.
So in exponential form it can be written as 22 x 19.

How many factors are there for 76?

Factors of 76 are 1, 2, 4, 19, 38, 76.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 76. Can you predict the answer?

5 factor(s) of 76 are 1, 2, 4, 19, 38.

Sammy is puzzled while calculating the prime factors of 76. Can you help him find them?

Factors of 76 are 1, 2, 4, 19, 38, 76.
Prime factors of 76 are 2, 2, 19

What is prime factorization of 76?

Prime factorization of 76 is 2 x 2 x 19 = 22 x 19.