Factors of 73
When you try and find the factors of a prime number, you will always get 1 and that number as its factors. This is the fundamental rule of a prime number. Let's take an example of 73, the number you will study in this lesson. Factors of 73 are the numbers which when multiplied in pairs give the product as 73. In this lesson, we will calculate the factors of 73, prime factors of 73, and factors of 73 in pairs along with solved examples for a better understanding.
Factors of 73: 1 and 73.
Prime Factorization of 73: 1 × 73
1.  What Are the Factors of 73? 
2.  How to Calculate Factors of 73? 
3.  Factors of 73 by Prime Factorization 
4.  Factors of 73 in Pairs 
5.  FAQs on Factors of 73 
What Are Factors of 73?
The factor of a number is that number that divides it completely i.e., leaving no remainder. For example, to find the factors of the number 73, we will have to perform division on 73 and find the numbers which divide 73 completely, leaving no remainders. Since 73 is a prime number so it has only two factors 1 and 73.
The given diagram provides the representation of the above definition:
Important Notes:
 If the number of factors of any number n is odd, then the number n is a perfect square.
 The factors of a number are only considered to be positive factors if not specified.
 Any number always has two factors, 1 and the number itself.
 The numbers that have more than 2 factors are called composite numbers.
How to Calculate Factors of 73?
To calculate the factors of any number, here in this case 73, we need to find all the numbers that would divide 73 without leaving any remainder. Since, 73 is a prime number so we start with the number 1, and end with 73. The number 1 and 73 itself would always be a factor of the 73.
Refer to the following table to check division 73 by its factors:
Division  Factor 

73 ÷ 1 = 73 
Remainder = 0 Factor = 1 
73 ÷ 73=1 
Remainder = 0 Factor = 73 
Hence, the factors of 73 are 1 and 73.
Explore factors using illustrations and interactive examples
 Factors of 86  The factors of 86 are 1, 2, 43, 86
 Factors of 96  The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
 Factors of 76  The factors of 76 are 1, 2, 4, 19, 38, 76
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 73 by Prime Factorisation
We just saw 73 is a prime number. It has only 2 factors 1 and the number itself.
So the prime factorization of the number 73 is written as 1 × 73.
Factors of 73 in pairs
Pair of factors of number n is the set of two numbers which when multiplied together gives the number n. Positive factors of 73 are: 1, 73
Pair of positive factors of 73 are: (1, 73)
1 × 73 = 73
Negative factors of 73 are: 1, 73
Pair of negative factors of 73 is (1, 73).
1 × 73 = 73
The following table represents the calculation of pair factors of 73:
Factor Pair  Pair Factorization 

1 and 73 
1 × 73 = 73 
Solved Examples

Example 1 Miss Mary asked her student John to calculate the common factors of 73 and 219. Help John in finding out the common factors.
Solution
Factors for 73 are 1, and 73
Factors of 219 are 1, 3, 73 and 219Common factors of 73 and 219 are 1 and 73

Example 2 Jacob says that (1,73) is a factor pair of 73, while Diana says (1,73) is a factor pair of 73, who is correct?
Solution
To check whether the above pairs are factor pairs of 73 or not we have to multiply them.
Jacob's factor pair is (1, 73)
1 × 73 = 73
73 is not equal to 73
Diana's factor pair is (1, 73)
1 × 73 = 73
73 is equal to 73Hence, (1,73) is a pair factor of 73.

Example 3 73 is a prime number, how many factors does 73 × 2 have?
Solution
73^{2} = 73 × 73 = 5329
Therefore, 73^{2 } has 3 factors 1, 73, 5329.
FAQs on factors of 73
1. What are the common factors of 73 and 146?
The common factors of 73 and 146 are 1 and 73.
2. What number is divisible by 73?
A number is divisible by its factors. The factors of 73 are 1 and 73.
3. Is 73 prime or composite?
73 is a prime number because it has only two factors, 1 and 73.
4. What is the highest common factor of 73 and 72?
Factors for 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors for 73 are 1, and 73
Hence, HCF of 73 and 72 =1