Factors of 52 Using Prime Factorization
What are the Factors of 52?
We will now learn more on the factors of 52 in the following article and to solve some interesting problems.
The numbers that divide 52 completely, that is, without leaving any remainder, are known as factors of 52.
Factors of 52 are: 1, 2, 4, 13, 26, and 52.
Factors completely divide the number. As a result, they can’t be fractions or decimals.
Factor List for the Number 52
Divisor | Is the Number a Factor of 52? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 52 = 52 |
2 | Yes, 52 is even | 2 x 26 = 52 |
3 | No, 5 + 2 = 7 is not divisible by 3 | - |
4 | Yes, 52 \(\div\) 4 = 13R0 | 4 x 13 = 52 |
5 | No, ones digit is not 0 or 5 | - |
6 | No, 52 \(\div\) 6 = 8R4 | - |
7 | No, 52 \(\div\) 7 = 7R3 | - |
8 | No, 52 \(\div\) 8 = 6R4 | - |
9 | No, 52 \(\div\) 9 = 5R7 | - |
10 | No, ones digit is not 0 | - |
11 | No, 52 \(\div\) 11 = 4R8 | - |
12 | No, 52 \(\div\) 12 = 4R4 | - |
13 | Yes, 52 \(\div\) 13 = 4R0 | 13 x 4=52 |
At 13, we can see that the multiplication equation has repeated. Therefore, we have derived all the factors of 52.
So, factors of 52: 1, 2, 4, 13, 26, and 52
Prime Factorization of 52
Prime factorization can be used to find the prime factors of 52.
52 is a composite number as it has more than two factors. Hence to factorize 52 and find its factors, we keep dividing 52 by prime factors till we get the result as 1. Let’s take a look at how to factorize 52:
- The first step is to divide 52 by its smallest prime factor, which is 2.
52 \(\div\) 2 = 26
26 \(\div\) 2 = 13
- Again, dividing 13 by 13,
13 \(\div\) 13 = 1
Hence, the factor tree of 52 can be written as:
The prime factorization of 52 is 2 x 2 x 13 or \(2^2\) x 13, where 2 and 13 are prime numbers.
Read More:
Factor Pairs of 52
When a pair of factors of 52 are multiplied together to result in 52, they are said to be factor pairs or pair factors of 52.
Positive Factors of 52 | Positive Factor Pairs of 52 |
|---|---|
1 x 52 | (1, 52) |
2 x 26 | (2, 26) |
4 x 13 | (4, 13) |
Solved Factors of 52 Examples
Example 1: Find the common factors of 36 and 52.
Solution:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 52: 1, 2, 4, 13, 26, and 52.
So, the common factors of 36 and 52 are 1, 2 and 4.
Example 2: On a table, there are 52 baseballs. Tom is responsible for distributing the baseballs to his four players equally. What is the total number of baseballs that each player will receive after the distribution?
Solution:
Total number of baseballs = 52
Total number of players = 4
Number of baseballs each player gets = \(\frac{52}{4}\) = 13
So, each player will get 13 baseballs after distribution.
Example 3: Is 5 a factor of 52?
Solution:
5 does not divide 52 exactly. It leaves a remainder of 2.
So, 5 is not a factor of 52.
Prime factorization of 52 is 2 x 2 x 13. As a result, the greatest prime factor of 52 is 13.
Yes, 52 is a composite number as it has factors of 2, 4, 13 and 26 other than 1 and itself, which is 52.
The factors of 52 are 1, 2, 4, 13, 26, and 52.
So, the least factor of 52 is 1 and the greatest factor is 52 itself.
The following are some important properties of factors:
- An exact divisor of a number is called a factor.
- Every number has a factor of one.
- The greatest factor of a number is the number itself.
- A factor is never greater than the number itself.