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Factors Of 53
Did you know that 53 is written as 35 in its hexadecimal representation, which is the number with the same digits as 53 in reversed order? In this lesson, we will calculate the factors of 53, prime factors of 53, and factors of 53 in pairs along with solved examples for a better understanding.
 Factors of 53: 1 and 53
 Prime Factorization of 53: 53 = 53^{1}
1.  What Are the Factors of 53? 
2.  How to Calculate Factors of 53? 
3.  Factors of 53 by Prime Factorization 
4.  Factors of 53 in Pairs 
5.  FAQs on Factors of 53 
What Are the Factors of 53?
The factors of 53 are numbers (integers) that divide 53 without any remainder. For example, 53 is a factor of itself because 53 divides itself without any remainder.
Interestingly, 1, which is the quotient of the above division, is also a factor of 53. Check if you get 0 as the remainder on dividing 53 by 1 using long division.
Tips and Tricks:
 A factor of a number is always less than or equal to the number.
 1 and the number itself are always the factors of a number.
How to Calculate the Factors of 53?
In the previous section, we learned that factors can be found using division. Since multiplication is the reverse process of division, we can find the factors using multiplication as well.
To find the factors of 53, we write 53 as a product of any two numbers in all the possible ways. The numbers that we multiply to get 53 are called the factors of 53.
53 cannot be written as the product of any two numbers other than these two ways.
Hence, the factors of 53 are 1 and 53.
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 56  The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
 Factors of 54  The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
 Factors of 63  The factors of 63 are 1, 3, 7, 9, 21, 63
 Factors of 55  The factors of 55 are 1, 5, 11, 55
 Factors of 12  The factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 53 by Prime Factorization
Prime factorization of 53 is expressing it as the product of prime numbers. But as we discussed in the previous section, 53 has only two factors, 1 and 53.
Thus, 53 itself is a prime number.
So the prime factorization of 53 is 53 =53^{1}
Also, we know that 1 is a factor of every number. Thus, factors of 53 are 1 and 53.
Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed it, for prime numbers, there are no other factors. But how do we find the factors of a composite number using prime factorization? Let's learn this through some examples.
Challenging Questions:
 Liam wants to plant 24 rose plants, 30 lily plants, and 42 jasmine plants in his garden. If he wants to put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants he can put in one row?
Factors of 53 in Pairs
The pair factors of 53 are obtained by writing 53 as a product of two numbers in all possible ways. In each product, both multiplicands are the factors of 53.
Product That Results in 53 
Pair Factors of 53 

1 × 53 
1, 53 
53 × 1 
53, 1 
Both pairs are the same. The negative pair factor of 53 is (1, 53).
Factors of 53 Solved Examples

Example 1: Jennifer is stuck with solving the following riddle. Can you help her?
"I am a prime number. I lie between 50 and 60. I am close to 50, but not to 60. Who am I?"
Solution:
The prime numbers between 50 and 60 are 53 and 59.
Among these two numbers, the number that is closer to 50 is 53.
Thus, the answer to the riddle is 53. 
Example 2: Help Jonathan write all the factors of 53 and 24 and find all the common factors.
Solution:
Let us list them and find the common factors.
Factors of 53: 1, 53
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24The common factor is 1.
FAQs on Factors of 53
What are the factors of 53?
The factors of 53 are 1 and 53.
Is 53 a Prime Number?
Yes, 53 is a prime number as it has exactly two factors (1 and 53).
Is 106 a factor of 53?
No, 106 is not a factor of 53.
What are the odd factors of 53?
The odd factors of 53 are 1 and 53.
What are the common factors of 53 and 77?
Factors of 53 = 1, 53
Factors of 77 = 1, 7, 11, 77
The common factor of 53 and 77 is 1.
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