Factors of 7 | How to Find the Factors of 7 by Prime Factorization Method? (2024)

The factors of 7 are the numbers that when multiplied in pairs, give the number 7. The factors of 7 can be positive as well as negative. For example, the pair factor of 7 can be (1, 7) as well as (-1, -7). If we multiply the -1 and -7, it will result in the original number 7. Here, we are going to learn what are the factors of 7, the pair factors and the prime factors of 7, and the procedure for finding the factors of 7 using the prime factorization method.

Table of Contents:

• What are the Factors of 7?
• Pair Factors of 7
• Factors of 7 by Division Method
• Prime Factorization of 7
• Solved Examples
• FAQs

What are the Factors of 7?

The factors of 7 are the numbers that divide the original number exactly without leaving the remainder. In other words, the factors of 7 are the numbers, which on multiplication in pairs gives the original number. As the number 7 is a prime number, it should have only two factors, such as one and the number itself. Hence, the factors of 7 are 1 and 7.

Pair Factors of 7

The pair factors of 7 are the multiplication of the pair of numbers that results in the original number 7. As discussed above, the pair factors of 7 can be positive as well as negative. The following are the positive and negative pair factors of 7.

Positive Pair Factors of 7

Negative Pair Factors of 7

Factors of 7 by Division Method

To find the factors of 7 by the division method, start dividing the number 7 by 1 and continue by dividing the number by the next consecutive numbers. As the number 7 is an odd and the prime number, the factors of 7 are 1 and 7 only. Also, the factors of 7 should be an odd number.

• 7/1 = 7 (Factor = 1 and Remainder =0)
• 7/7 = 1 (Factor = 7 and Remainder =0)

Prime Factorization of 7

We know that the factorization of numbers means the process of writing the numbers as the product of its factors. Similarly, the process of writing the number as the product of its prime factors is called the prime factorization method.

Now, let us learn how to find the prime factors of 7 using the prime factorization method.

Step 1: Write down the number 7, and take the pair factor of 7, say (1, 7)

Step 2: Here, both the factors, such as 1 and 7 are prime numbers and hence, they cannot be split further.

Hence, the prime factorization of 7 can be written as the product of 1 and 7.

Therefore, the prime factorization of 7 is 7 or 7¹.

Note: If any of the factors in pairs (or) both the factors in a pair are composite numbers, split the composite numbers into its prime factors, and then the prime factors should be multiplied.

Video Lesson on Prime Factors

Examples

Example 1:

Find the common factors of 7 and 49.

Solution:

The factors of 7 are 1 and 7.

The factors of 49 are 1, 7 and 49.

Therefore, the common factors of 7 and 49 are 1 and 7.

Example 2:

Find the common factors of 7 and 63.

Solution:

Factors of 7 = 1 and 7

Factors of 63 = 1, 3, 7, 9, 21 and 63

Hence, the common factors of 7 and 63 are 1 and 7.

Example 3:

Find the common factors of 7 and 54.

Solution:

The factors of 7 are 1 and 7.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54.

Therefore, the common factor of 7 and 54 is 1.