Factors of 74
Do you know 74 is semiprime? It has only 2 factors which are prime numbers apart from 1 and 74. In this lesson, we will learn to calculate the factors of 74, prime factors of 74, and factors of 74 in pairs along with solved examples for a better understanding.
 Factors of 74: 1, 3, 37 and 74
 Prime Factorization of 74: 74 = 2 × 37
1.  What Are the Factors of 74? 
2.  How to Calculate the Factors of 74? 
3.  Factors of 74 by Prime Factorization 
4.  Factors of 74 in Pairs 
5.  FAQs on Factors of 74 
What are the Factors of 74?
Factors of 74 are the numbers which when multiplied in pairs give the product as 74. Factors of a number n are the numbers that completely divides the number n.It means that if the remainder in n/a is zero then a is the factor of n.
We are here talking about the factors of the number 74. Let's first see the numbers that completely divide 74.
The positive numbers are 1, 2, 37, 74 which divides 74 completely. Hence, positive factors of 74 are 1, 2, 37 and 74 and negative factors of 74 are 1, 2, 37, and 74.
How to Calculate the Factors of 74?
All the numbers which divide 74 without leaving any remainder are its factors. Let us try dividing 74 by counting numbers (1,2,3 etc, and see when the remainder is 0)
 74 ÷ 1 quotient = 74 and remainder = 0 so 1 is a factor of 74.
Since 74 is an even number 2 divides 74 without any remainder.
 74 ÷ 2 quotient = 37, remainder = 0, so 2 is a factor of 74.
Proceeding further we see that the numbers 1, 2, 37, and 74 exactly divide 74 leaving no remainder.
The negative numbers are 1, 2, 37, 74 which divides 74 completely.
Hence, the factors of 74 are 1, 2, 37 and 74.
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 37  The factors of 37 are 1, 37
Factors of 74 by Prime Factorization
In the prime factorization method, we write 74 as a product of prime numbers. The prime numbers are the numbers that have only two factors;1 and the number itself. For example: 2, 3, 5, 7, 11, 13.
The factor tree of 74 is shown below:
We can't branch further because we have landed on the prime numbers, so 74 has no other prime factors. Prime factors of 74 are 2 and 37.
Factors of 74 in Pairs
The pair of factors of number n is the set of two numbers which when multiplied together gives the number n. Positive factors of 74 are: 1, 2, 37, 74
Pairs of positive factors of 74 are: (1, 74), (2, 37)
 1 × 74 = 74
 2 × 37 = 74
Negative factors of 74 are: 1, 2, 37, 74. Pairs of negative factors of 74 are: (1, 74), (2, 37).
 1 × 74 = 74
 2 × 37 = 74
Challenging Questions:
 Can 74 toffees be evenly divided and shared with 24 kids?
 How many positive integers, less than 74 are coprime with 74?
Important Notes:
 Factors of 74 are 1, 2, 37 and 74
 74 is a semiprime number as it can be expressed as a product of two prime numbers.
 If a number n has an odd number of positive factors then n is a perfect square.
 There are no factors of a number n between (n, n/2).
Factors of 74 Solved Examples

Example 1: Help Donald to find the sum of all the positive factors of 74
Solution:
The positive factors of 74 are: 1, 2, 37, and 74. Thus, sum of all the factors is 1 + 2 + 37 + 74 = 114.
Hence, Sum of all the positive factors of 74 is 114. 
Example 2: Find the common factors of 74, 86 and 72.
Solution:
The factors of 74 are 1, 2, 37, and 74. The factors of 86 are 1, 2, 43, and 86. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Hence, the factors common to 74, 86 and 72 are 1 and 2. 
Example 3: Julia wants to add a natural number to 20 so that it will become a factor of 74, what number should she add.
Solution:
Let's suppose she adds x to 20. So x + 20 is a factor of 74.
Let's write down all the factors of 74 greater than 20: (37, 74)x + 20 = 37
x + 20 = 74
So, x can be 17, 54
FAQs on Factors of 74
What are the factors of 74?
The factors of 74 are 1, 2, 37 and 74.
What are all the factors of 74?
The positive factors of 74 are, 1, 2, 37, 74. The negative factors of 74 are, 1, 2, 37, 74.
What are the prime factors of 74?
The prime factors of 74 are 2 and 37.
Which is the smallest prime factor of 74?
The prime factors of 74 are 2 ad 37. 2 is the smallest prime fcator of 74.
What are the common factors of 74 and 51?
The factors of 74 are 1, 2, 37 and 74. The factors of 51 are 1, 3, 17, and 51. Thus, the common factor of 74 and 51 is 1.
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