# Factors of 104

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104

#### How to find factors of a number

 1.   Find factors of 104 using Division Method 2.   Find factors of 104 using Prime Factorization 3.   Find factors of 104 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 104

• Divide 104 by 1: 104 ÷ 1 : Remainder = 0
• Divide 104 by 2: 104 ÷ 2 : Remainder = 0
• Divide 104 by 4: 104 ÷ 4 : Remainder = 0
• Divide 104 by 8: 104 ÷ 8 : Remainder = 0
• Divide 104 by 13: 104 ÷ 13 : Remainder = 0
• Divide 104 by 26: 104 ÷ 26 : Remainder = 0
• Divide 104 by 52: 104 ÷ 52 : Remainder = 0
• Divide 104 by 104: 104 ÷ 104 : Remainder = 0

Hence, Factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104

#### 2. Steps to find factors of 104 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 104 using the division method, follow these steps:

• Step 1. Start dividing 104 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 104, which is 2. Divide 104 by 2 to obtain the quotient (52).
104 ÷ 2 = 52
• Step 3. Repeat step 1 with the obtained quotient (52).
52 ÷ 2 = 26
26 ÷ 2 = 13
13 ÷ 13 = 1

So, the prime factorization of 104 is, 104 = 2 x 2 x 2 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 104 as shown below:

So, the prime factorization of 104 is, 104 = 2 x 2 x 2 x 13.

#### 3. Find factors of 104 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 104 would be the two numbers which, when multiplied, give 104 as the result.

The following table represents the calculation of factors of 104 in pairs:

Factor Pair Pair Factorization
1 and 104 1 x 104 = 104
2 and 52 2 x 52 = 104
4 and 26 4 x 26 = 104
8 and 13 8 x 13 = 104

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 104. They are called negative pair factors.

Hence, the negative pairs of 104 would be ( -1 , -104 ) , ( -2 , -52 ) , ( -4 , -26 ) and ( -8 , -13 ) .

#### 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. 104 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 104.
• Every number is a factor of zero (0), since 104 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, 8, 13, 26, 52, 104 are exact divisors of 104.
• Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. Each factor divides 104 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 26, 52, 104 are all less than or equal to 104.

• What are the pair factors of 104?

Pair factors of 104 are (1,104), (2,52), (4,26), (8,13).

• What are five multiples of 104?

First five multiples of 104 are 208, 312, 416, 520, 624.

• What two numbers make 104?

Two numbers that make 104 are 2 and 52.

• What is the sum of all factors of 104?

The sum of all factors of 104 is 210.

• What are factors of -104?

Factors of -104 are -1, -2, -4, -8, -13, -26, -52, -104.

• What are factors of 104?

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.

• Is 104 a perfect square?

No 104 is not a perfect square.

• Which is the smallest prime factor of 104?

Smallest prime factor of 104 is 2.

• Which is greatest factor of 104?

The greatest factor of 104 is 52.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 104?

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.
Odd factors of 104 are 1, 13.
Hence product of odd factors of 104 is; 1 x 13 = 13.

Joey wants to write all the prime factors of 104 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 104 are 2, 2, 2, 13.
So in exponential form it can be written as 23 x 13.

How many factors are there for 104?

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 104. Can you predict the answer?

7 factor(s) of 104 are 1, 2, 4, 8, 13, 26, 52.

Sammy is puzzled while calculating the prime factors of 104. Can you help him find them?

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.
Prime factors of 104 are 2, 2, 2, 13

What is prime factorization of 104?

Prime factorization of 104 is 2 x 2 x 2 x 13 = 23 x 13.

Can you help Rubel to find out the product of the even factors of 104?

Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104.
Even factors of 104 are 2, 4, 8, 26, 52, 104.
Hence, product of even factors of 104 is; 2 x 4 x 8 x 26 x 52 x 104 = 8998912.