# Factors of 52

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

#### How to find factors of a number

 1.   Find factors of 52 using Division Method 2.   Find factors of 52 using Prime Factorization 3.   Find factors of 52 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 52

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

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

#### 2. Steps to find factors of 52 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 52 using the division method, follow these steps:

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

So, the prime factorization of 52 is, 52 = 2 x 2 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 52 as shown below:

So, the prime factorization of 52 is, 52 = 2 x 2 x 13.

#### 3. Find factors of 52 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 52 would be the two numbers which, when multiplied, give 52 as the result.

The following table represents the calculation of factors of 52 in pairs:

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

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 52. They are called negative pair factors.

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

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

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

• Which is the smallest prime factor of 52?

The smallest prime factor of 52 is 2.

• Is 52 a whole number?

Yes 52 is a whole number.

• What are the prime factors of 52?

The factors of 52 are 1, 2, 4, 13, 26, 52.
Prime factors of 52 are 2, 2, 13.

• What two numbers make 52?

Two numbers that make 52 are 2 and 26.

• What are multiples of 52?

First five multiples of 52 are 104, 156, 208, 260.

• What is the sum of all factors of 52?

The sum of all factors of 52 is 98.

• What are five multiples of 52?

First five multiples of 52 are 104, 156, 208, 260, 312.

• Is 52 a perfect square?

No 52 is not a perfect square.

• What is the greatest prime factors of 52?

The greatest prime factor of 52 is 13.

#### Examples of Factors

How many factors are there for 52?

Factors of 52 are 1, 2, 4, 13, 26, 52.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 52. Can you predict the answer?

5 factor(s) of 52 are 1, 2, 4, 13, 26.

Sammy is puzzled while calculating the prime factors of 52. Can you help him find them?

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

What is prime factorization of 52?

Prime factorization of 52 is 2 x 2 x 13 = 22 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 52. Can you help her?

Prime factors of 52 are 2, 2, 13.
Hence, the product of prime factors of 26.

Can you help Rubel to find out the product of the even factors of 52?

Factors of 52 are 1, 2, 4, 13, 26, 52.
Even factors of 52 are 2, 4, 26, 52.
Hence, product of even factors of 52 is; 2 x 4 x 26 x 52 = 10816.

Joy wants to calculate mean of all the factors of 52. Help him in finding the mean of 52.

Factors of 52 are 1, 2, 4, 13, 26, 52.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 52 is 1 + 2 + 4 + 13 + 26 + 52 = 98.
Hence, the mean of factors of 52 is 98 ÷ 6 = 16.33.