# Factors of 78

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78

#### How to find factors of a number

 1.   Find factors of 78 using Division Method 2.   Find factors of 78 using Prime Factorization 3.   Find factors of 78 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 78

• Divide 78 by 1: 78 ÷ 1 : Remainder = 0
• Divide 78 by 2: 78 ÷ 2 : Remainder = 0
• Divide 78 by 3: 78 ÷ 3 : Remainder = 0
• Divide 78 by 6: 78 ÷ 6 : Remainder = 0
• Divide 78 by 13: 78 ÷ 13 : Remainder = 0
• Divide 78 by 26: 78 ÷ 26 : Remainder = 0
• Divide 78 by 39: 78 ÷ 39 : Remainder = 0
• Divide 78 by 78: 78 ÷ 78 : Remainder = 0

Hence, Factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78

#### 2. Steps to find factors of 78 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 78 using the division method, follow these steps:

• Step 1. Start dividing 78 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 78, which is 2. Divide 78 by 2 to obtain the quotient (39).
78 ÷ 2 = 39
• Step 3. Repeat step 1 with the obtained quotient (39).
39 ÷ 3 = 13
13 ÷ 13 = 1

So, the prime factorization of 78 is, 78 = 2 x 3 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 78 as shown below:

So, the prime factorization of 78 is, 78 = 2 x 3 x 13.

#### 3. Find factors of 78 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 78 would be the two numbers which, when multiplied, give 78 as the result.

The following table represents the calculation of factors of 78 in pairs:

Factor Pair Pair Factorization
1 and 78 1 x 78 = 78
2 and 39 2 x 39 = 78
3 and 26 3 x 26 = 78
6 and 13 6 x 13 = 78

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 78. They are called negative pair factors.

Hence, the negative pairs of 78 would be ( -1 , -78 ) , ( -2 , -39 ) , ( -3 , -26 ) and ( -6 , -13 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 78 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, 3, 6, 13, 26, 39, 78 are exact divisors of 78.
• 1 is a factor of every number. Eg. 1 is a factor of 78.
• Every number is a factor of zero (0), since 78 x 0 = 0.

• How do you find factors of a negative number? ( eg. -78 )?

Factors of -78 are -1, -2, -3, -6, -13, -26, -39, -78.

• What is the sum of all factors of 78?

The sum of all factors of 78 is 168.

• What is prime factorization of 78?

Prime factorization of 78 is 2 x 3 x 13.

• What are the pair factors of 78?

Pair factors of 78 are (1,78), (2,39), (3,26), (6,13).

• What are six multiples of 78?

First five multiples of 78 are 156, 234, 312, 390, 468, 546.

• Is 78 a whole number?

Yes 78 is a whole number.

• Which is the smallest prime factor of 78?

Smallest prime factor of 78 is 2.

• What are five multiples of 78?

First five multiples of 78 are 156, 234, 312, 390, 468.

• Write all factors of 78?

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.

#### Examples of Factors

Joey wants to write all the prime factors of 78 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 78 are 2, 3, 13.
So in exponential form it can be written as 2 x 3 x 13.

How many factors are there for 78?

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 78. Can you predict the answer?

7 factor(s) of 78 are 1, 2, 3, 6, 13, 26, 39.

Sammy is puzzled while calculating the prime factors of 78. Can you help him find them?

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.
Prime factors of 78 are 2, 3, 13

What is prime factorization of 78?

Prime factorization of 78 is 2 x 3 x 13 = 2 x 3 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 78. Can you help her?

Prime factors of 78 are 2, 3, 13.
Hence, the product of prime factors of 78.

Can you help Rubel to find out the product of the even factors of 78?

Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.
Even factors of 78 are 2, 6, 26, 78.
Hence, product of even factors of 78 is; 2 x 6 x 26 x 78 = 24336.