Factors of 50
50 is the smallest number that is the sum of two nonzero square numbers in two distinct ways: 50 = 1^{2} + 7^{2 }= 5^{2} + 5^{2}. It is also the sum of three squares: 50 = 3^{2} + 4^{2} + 5^{2} and the sum of four squares: 50 = 6^{2} + 3^{2} + 2^{2 }+ 1^{2}.
 Factors of 50: 1, 2, 5, 10, 25, 50
 Prime Factorization of 50: 2 × 5 × 5
1.  What Are the Factors of 50? 
2.  How to Calculate the Factors of 50? 
3.  Factors of 50 by Prime Factorization 
4.  Tips and Tricks 
5.  Factors of 50 in Pairs 
6.  Important Notes 
What Are the Factors of 50?
 Factors of 50 are the numbers which on dividing 50 leave no remainder. Since 50 is a composite number, it has more than two factors. Let us find the factors of 50.
 Let's consider the numbers that can divide 50 without leaving any remainder.
 We will start with 1, then move on to 2, 3,.. up to 25 (which is exactly half of 50).
 50 has a total of 6 factors. The factors of 50 obtained this way are 1, 2, 5, 10, 25, and 50.
How to Calculate the Factors of 50?
 Factors of 50 can be found out by various methods. We know that 1 and 50 are the factors of 50, as it is with any number.
 Let us find the prime factors of 50 by the division method. Keep dividing 50 starting from 2 up to 25 (half of 50).
Dividing  Result 

50 ÷ 1 
Gives remainder 0. So, 1 is a factor. 
50 ÷ 2 
Gives remainder 0. So, 2 is a factor. 
50 ÷ 5 
Gives remainder 0. So, 5 is a factor. 
50 ÷ 10 
Gives remainder 0. So, 10 is a factor. 
50 ÷ 25 
Gives remainder 0. So, 25 is a factor. 
50 ÷ 50 
Gives remainder 0. So, 50 is a factor. 
Explore factors using illustrations and interactive examples.
 Factors of 56: The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
 Factors of 30: The factors of 30 are 1 , 2 , 3, 5, 10 ,15,and 30.
 Factors of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 2,16, 24, and 48.
 Factors of 75: The factors of 75 are 1, 3, 5, 15, 25, and 75.
 Factors of 10: The factors of 10 are 1, 2, 5, and 10.
Factors of 50 by Prime Factorization
Prime factorization of a number refers to representing a number in the form of the products of its prime factors.
 A factor tree is a special branching diagram where we find the factors stepbystep for the given number.
 Then we find the factors of those resulting numbers, repeating this step until we cannot factor them anymore.
 The ends of the branches of the factor tree give all the prime factors of the original number.
 Thus, the prime factorization of 50 is written as 2× 5 × 5 or 2 × 5 ^{2}
 Now that we have done the prime factorization of our number, we can multiply them and get the other possible composite factors.
Tips and Tricks
 50 = 2 × 5 × 5 = 2 × 5^{2}
 To get the total numbers of factors of 50:
 Add 1 to the exponents of 2 and 5, and multiply their sums: (1 + 1) × (2 + 1) = 2 x 3 = 6
 Thus, 50 has 6 factors and they are 1, 2, 5, 10, 25, and 50.
Factors of 50 in Pairs
 Pair factors of the number 50 are whole numbers which give the original number, i.e., 50 when multiplied.
 Pair factors can be either positive or negative but they cannot be a fraction or a decimal number.
 (1, 50 ), (1, 50), (2, 25), (2, 25), (5, 10), (5, 10)
Positive Factor Pairs  Negative Factor Pairs 
1 × 50  1 × 50 
2 × 25  2 × 25 
5 × 10  5 × 10 
Important Notes:
 Only whole numbers and integers can be factors.
 Only composite numbers can have more than two factors.
 Every factor of a given number is either less than or equal to the given number.
Factors of 50 Solved Examples

Example 1: What is the sum of all the factors of the number 50 including 50?
Solution:
Factors of 50: 1, 2, 5, 10, 25, 50
Sum of all the given factors = 1 + 2 + 5 + 10 + 25 + 50 = 93

Example 2: Write all the factors of 50 which are also the factors of 450.
Solution:
Factors of 50 = 1, 2, 5, 10, 25, 50
Factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Hence, the common factors of 50 and 450 are 1, 2, 5, 25, and 50.
FAQs on Factors of 50
What are the factors of 50?
The factors of 50 are the numbers that make 50 together. They leave no remainder when they divide 50. The factors of 50 are 1, 2, 5,10, 25, and 50.
What are the common factors of 50 and 60?
 Factors of 50: 1, 2, 5, 10, 25, 50
 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
 Therefore, the common factors of 50 and 60 are 1, 2, 5, and 10.
What are the common factors of 50 and 35?
 Factors of 35: 1, 5, 7, 35
 Factors of 50: 1, 2, 5, 10, 25, 50
 Therefore, the common factors of 35 and 50 are 1 and 5.
What is the greatest prime factor of 50?
 Factors of 50: 1, 2, 5, 10, 25, 50
 The greatest prime factor of 50 is the greatest prime number among the factors of 50.
 Hence, the greatest prime factor of 50 is 5.
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