Factors of 53 Using Prime Factorization
What are the Factors of 53?
Natural numbers that can divide a number exactly are known as the factors of that number. When a number is divided by its factor the remainder is zero and the quotient is also a factor of that number.
The number 53 has a total of two factors: 1 and 53.
Factors of 53 | Factor pairs of 53 | Prime Factorization of 53 |
|---|---|---|
1 , 53 | (1, 53) | 1 \(\times\) 53 |
Factor List of 53
By applying divisibility rules and division facts we can create the factor list of 53.
Divisor | Is the number a factor of 53 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all number | 1 \(\times\) 53 = 53 |
2 | No, 53 is odd | —------ |
3 | No, 5 + 3 = 8 is not divisible by 3 | —------ |
4 | No, 53 \(\div\) 4 = 13 Remainder = 1 | —------ |
5 | No, the ones digit is neither 0 nor 5 | —------ |
6 | No, 53 is neither divisible by 2 nor by 3 | —------ |
7 | No, 53 \(\div\) 7 = 7 and Remainder = 4 | —------ |
8 | No, 53 \(\div\) 8 = 6 and Remainder = 5 | —------ |
9 | No, Since 53 is not divisible by 3 | —------ |
10 | No, ones place digit is not 0 | —------ |
11 | No, 53 \(\div\) 11 = 4 and Remainder = 9 | —------ |
If we continue checking for numbers greater than 11 we will notice that the factor pairs start to repeat. Hence, we can stop checking at this step.
[Note: If we divide 53 by 12, we get the quotient and remainder as 4 and 5, respectively. So, 12 is not a factor of 53. Similarly, you can check for other numbers as well.]
Prime Factorization of a Number
The factor tree below can be used to represent the prime factorization of 53:
Prime factorization of 53 is 1 × 53.
Also, we can say that 1 and 53 are the prime factors of 53.
Read More:
Factor Pairs of 53
Pair factors or factor pairs of 53 is a set of two factors of 53 which when multiplied gives 53 as the product. For example, (1, 53) is a factor pair of 53, as both 1 and 53 are factors of 53 and, 1 \(\times\) 53 = 53.
Factors of 53 | Factor pairs of 53 |
|---|---|
1, 53 | (1, 53) |
Solved Factors of 53 Examples
Example 1: You want to organize 53 pictures into a rectangular array on a wall. How many different arrays can you make?
Solution: To find the number of arrays you can make, find the number of factor pairs of 53.
There is only one factor pair of 53 which is (1, 53).
you can use each factor pair to make 2 arrays.
So, there are two ways to organize the pictures in a rectangular array.
(a) 1 picture in a row and 53 pictures in a column.
(b) 1 picture in a column and 53 pictures in a row.
Example 2: What is the prime factorization of the number 53?
Solution: 1 × 53 is the prime factorization of 53.
Example 3: Is 7 a factor of 53?
Solution: No,7 is not a factor of 53. Because, when we divide 53 by 7 we will get a quotient as 7 and remainder as 4. Since, the remainder is not zero, 7 is not a factor of 53.
Example 4: Find the highest common factors of 53 and 106.
Solution: The prime factorization of 106 is as below
106 = 1 \(\times \) 2 \(\times \) 53
The prime factorization of 53 = 1 \(\times \) 53.
Hence, we can see the highest common factor of 53 and 106 = 53.
No, an odd number can not have an even factor.
For Example: 15 is an odd number, its factors are: 1, 3, 5 and 15.
Yes, an even number can have odd factors.
For example:
Factor of 26: 1, 2 ,13 [here 1 and 13 are odd factors]
Factor of 52: 1, 2, 4, 13 [here 13 is odd factors]
No, the number of factors must be less than the number itself. The number of factors of any number is limited, that is, finite.
Factors of any number will be the divisors that exactly divide the number. This indicates that zero is the remainder in a division operation between a number and its factor.
Prime factors are factors that are prime numbers themselves.
Example:
Factors of 45 : 1, 3, 5, 9, 15, 45
Here all above numbers are called as factors of 45 but 3 and 5 are the prime factors of 45.