Find Prime Factorization/Factors Of 74 - Cuemath

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, 2, 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).