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 = 2^{2} × 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.
 Divide the number by 2 or find half of the number. If the result is a decimal, round it to the nearest integer.
 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.
 We do not need to divide the given number by the quotients of the divisions that gave the remainder 0.
 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 twothird 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.
Factors  Pair Factors 

1 × 52 = 52 
(1, 52) 
2 × 26 = 52 
(2, 26) 
4 × 13 = 52 
(4, 13) 
The factors can be negative as well.
The negative pair factors of 52 are (1, 52), (2, 26), and (4, 13).
Factors of 52 Solved Examples

Example 1: Mason asked his friend to name any two factors of 52 within 30 seconds.
Mason's friend thought and immediately gave him two factors of 52. What could be those two factors?
Solution:
Every number will definitely have a minimum of two factors, 1 and itself.
So, without thinking too much, we can say that 1 and 52 are the factors of 52.
Hence, the two factors of 52 that Mason's friend mentioned are probably 1 and 52.

Example 2: Help Noah find the sum of all the positive factors of 52.
Solution:
Positive factors of 52 are 1, 2, 4, 13, 26, and 52.
The sum of all the factors is 1 + 2 + 4 + 13 + 26 + 52 = 98
Hence, the sum of all the positive factors of 52 is 98.

Example 3: How many factors are there for 52?
Solution:
The factors of 52 are 1, 2, 4, 13, 26, 52. Therefore, 52 has 6 factors.
FAQs on Factors of 52
What are the Factors of 52?
The factors of 52 are 1, 2, 4, 13, 26, 52 and its negative factors are 1, 2, 4, 13, 26, 52.
What are the Prime Factors of 52?
The prime factors of 52 are 2, 13.
What is the Greatest Common Factor of 52 and 4?
The factors of 52 and 4 are 1, 2, 4, 13, 26, 52, and 1, 2, 4 respectively.
Common factors of 52 and 4 are [1, 2, 4].
Hence, the Greatest Common Factor (GCF) of 52 and 4 is 4.
How Many Factors of 49 are also common to the Factors of 52?
Since the factors of 52 are 1, 2, 4, 13, 26, 52, and factors of 49 are 1, 7, 49. Hence, 52 and 49 have only one common factor which is 1. Therefore, 52 and 49 are coprime.
What is the Sum of the Factors of 52?
Factors of 52 are 1, 2, 4, 13, 26, 52 and, the sum of all these factors is 1 + 2 + 4 + 13 + 26 + 52 = 98
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