Factors of 93
Factors of 93 are the numbers which when multiplied in pairs give the product as 93. There are 4 factors of 93 in all which can be both positive and negative. Did you know the number 93 is the first number in the third triplet of consecutive semiprimes, 93, 94, and 95? In this lesson, we will calculate the factors of 93, its prime factors, and its factors in pairs along with solved examples for a better understanding.
 Factors of 93: 1, 3, 31, 93
 Negative Factors of 93: 1, 3, 31, 93
 Prime Factorization of 93: 93 =^{ }3 × 31
1.  What are Factors of 93? 
2.  How to Calculate Factors of 93? 
3.  Factors of 93 by Prime Factorization 
4.  Factors of 93 in Pairs 
5.  Important Notes 
6.  Challenging Questions 
7.  FAQs on Factors of 93 
What are Factors of 93?
Factors of a number n are the numbers that completely divide the number n. It means that if the remainder in n ÷ a is zero, then a is the factor of n. We are talking here about factors of the number 93. Let's first see the numbers that completely divide 93. The numbers that divide 93 completely are 1, 3, 31, 93
Hence, the factors of 93 are 1, 3, 31, and 93
How to Calculate Factors of 93?
Factors of any number n can be calculated by many methods, one of the methods is dividing the number by the smallest of the factors. Factors of number 93 can be calculated as follows:
 Write the smallest factor of 93 (except for 1). The smallest factor of 93 is 3.
 Divide 93 by 3
 93 ÷ 3 = 31
 So, 3 and 31 are the factors of 93.
 Include 1 and the number itself to write all the factors.
Therefore, factors of 93 are 1, 3, 31, 93. Explore factors using illustrations and interactive examples:
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 97  The factors of 97 are 1, 97
 Factors of 43  The factors of 43 are 1, 43
 Factors of 92  The factors of 92 are 1, 2, 4, 23, 46 and 92
 Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36 and 72
 Factors of 34  The factors of 34 are 1, 2, 17, 34
Factors of 93 by Prime Factorization
The prime factorization method to calculate factors of any number is one of the most important methods. Many students prefer using prime factorization while performing calculations.
In the prime factorization method, we can only factorize a number into its prime factors. Prime numbers are the numbers that have only two factors 1 and the number itself. For example, 2, 3, 5, 7, 11, 13....
93 =^{ }3 × 31. Here, 3 and 31 are prime factors of 93.
Factors of 93 in Pairs
The pair of factors of number n is the set of two factors of n which when multiplied together gives the number n.
Factors of 93 are 1, 3, 31, 93:
 Positive factors of 93 in pairs are: (1, 93), (3, 31)
 1 × 93 = 93
 3 × 31 = 93
Negative factors of 93 are 1, 3, 31, 93:
 Negative factors of 93 in pairs are: (1, 93), (3, 31)
 1 × 93 = 93
 3 × 31 = 93
Important Notes:
 The prime factors of a number are different from their factors.
 If a number n has an odd number of positive factors then n is a perfect square.
 1 and the number itself is also the factor of any number.
 There are no factors of a number n between (n, n/2).
 The number that has more than 2 factors are called composite numbers.
 1 is not a prime number, 2 is the smallest prime number.
Challenging Questions:
 Kristin, a kindergarten teacher, taught her students that there exist two prime numbers such that when adding them the result obtained is 93. Is she correct? If not, then find out a proper explanation.
Factors of 93 Solved Examples

Example 1: Help Jim to find the sum of all the positive factors of 93.
Solution:
Positive factors of 93 are 1, 3, 31, 93. The Sum of all the factors is = 1 + 3 + 31 + 93 = 128
Hence, the sum of all the positive factors of 93 is 128

Example 2: Tim says that there exist only two common factors between 99 and 93, while Paul says there exist three common factors between these numbers, who is correct?
Solution:
Let's first write the factors of 99 and 93
 Factors of 99 are: 1, 3, 9, 11, 33, 99
 Factors of 93 are: 1, 3, 31, 93
 Common factors are 1 and 3
There are two common factors between 99 and 93. Hence, Tim is correct, 99 and 93 have two common factors

Example 3: If the factors of 93 are arranged in ascending order, the product of the two middle factors obtained is P and if the factors are arranged in descending order, the product of the two middle factors obtained is Q. Check whether P = Q or not.
Solution:
Factors of 93 are 1, 3, 31, 99. Factors of 93 arranged in ascending order: 1, 3, 31, 99
The middle two factors are: 3 and 31 3 × 31 = 93
 P = 93
Factors of 93 arranged in descending order: 93, 31, 3, 1. Middle two factors are: 31 and 3
 3 × 31 = 93
 Q = 93
Hence, P=Q.
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FAQs on Factors of 93
What are the Factors of 93?
Factors of 93 are 1, 3, 31, 93.
What are the Prime Factors of 93?
The prime factors of 33 are 3 and 11
What are the Common Factors of 93 and 57?
The factors of 93 are 1, 3, 31, 93. Similarly, the factors of 57 are 1, 3, 19, 57
The common factors of 93 and 57 are 1 and 3.
Is 93 a Prime or a Composite Number?
93 is a composite number as it has factors other than 1 and 31
What are the Common Factors of 93 and 36?
Factors of 93 = 1, 3, 31, 93 and the factors of 36 = 1 , 2, 3, 4, 6, 9, 12, 18, and 36
Therefore, the common factors of 93 and 36 are 1 and 3.
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