Factors of 52

Factors of 52 are the list of integers that we can split evenly into 52. There are overall 6 factors of 52 among which 52 is the biggest factor and 1, 2, 4, 13, 26 and 52 are positive factors. The Prime Factors of 52 are 1, 2, 4, 13, 26, 52 and its Factors in Pairs are (1, 52), (2, 26) and (4, 13).

• Factors of 52: 1, 2, 4, 13, 26 and 52
• Negative Factors of 52: -1, -2, -4, -13, -26 and -52
• Prime Factors of 52: 2, 13
• Prime Factorization of 52: 2 × 2 × 13 = 2² × 13
• Sum of Factors of 52: 98

What Are the Factors of 52?

The factors of 52 are the numbers (integers) that divide 52 without leaving any remainder.

For example, when 52 is divided by 13, the remainder is 0.

Hence, 13 is a factor of 52.

The steps to find the factors of any number are given below.

1. Divide the number by 2 or find half of the number. If the result is a decimal, round it to the nearest integer.
    
2. Divide the given number by all numbers from 1 to the resultant number that you have obtained in step 1 and see which of them would give 0 as the remainder.
   This is because numbers beyond "half of the given number" cannot be the factors of the given number.
    
3. We do not need to divide the given number by the quotients of the divisions that gave the remainder 0.
    
4. List the divisors and quotients of all such divisions. These are the factors of the number.

Finding Factors of 52

Half of 52 is 26.

We divide 52 by each number from 1 to 26 leaving the quotients of the divisions that give the remainder 0.

Then the divisions with 0 as the remainder are:

1 ÷ 52 = 52

2 ÷ 52 = 26

4 ÷ 52 = 13

In the above examples, quotient 52, 26, and 13 is also a factor.

Thus, the factors of 52 are 1, 2, 4, 13, 26, and 52.

Tips and Tricks:

• When you divide a number by its factor, the quotient of the division is also a factor.
  When we divide 52 by 13, we get 4 as the quotient. This quotient is also a factor. We do not need to separately divide 52 by 4 and see whether we get the remainder as 0.
• Every number has a minimum of two factors, 1 and itself.
• Applying divisibility rules to find factors makes our work easier when compared to doing manual division.

Explore factors using illustrations and interactive examples.

• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 
• Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
• Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
• Factors of 51 - The factors of 51 are 1, 3, 17, 51
• Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45

Factors of 52 by Prime Factorization

The prime factorization of 52 involves the products of prime numbers which give the result as 52.

Thus, the prime factorization of 52 is 52 = 2 × 2 × 13

From the prime factorization of 52, it is clear that 2 and 13 are factors of 52.

In fact, 2 and 13 are the prime factors of 52.

By multiplying different sets of multiplicands of the above prime factorization using different combinations, we get the other factors (composite factors) of 52.

2 × 2 = 4

2 × 13 = 26

  2 × 2 × 13 = 52

So 4, 26, and 52 are the composite factors of 52.

We know that 1 is a factor of every number.

Thus, the factors of 52 by prime factorization are 1, 2, 4, 13, 26, and 52

Challenging Questions:

• Can you find which factor of 52 is two-third of 52?
• Can decimals and fractions ever be the factors of 52?

Factors of 52 in Pairs

52 can be expressed as a product of two numbers in all possible ways.

In each product, both multiplicands are the factors of 52.

The factors can be negative as well.

The negative pair factors of 52 are  (-1, -52), (-2, -26), and (-4, -13).