Factors of 115

The factors of 115 are the numbers that divide 115 evenly without leaving any remainder value. In other words, the numbers which are multiplied in pairs resulting in the original number 115 are the factors of 115. For example, the pair factor of 115 is expressed as (1, 115) or (-1, -115). If we multiply a pair of negative numbers, such as multiplying -1 and -115, it will result in the number 115. Thus, the factors and the pair factors of 115 can be expressed in both positive and negative form. In this article, we are going to learn what are the factors of 115, positive and negative pair factors of 115, prime factors of 115 using the prime factorization method and many solved examples.

What are the Factors of 115?

In Mathematics, the numbers that divide the given number evenly without leaving any remainder are called the factors of a number. Thus, the factors of 115 are the list of numbers that divide 115 evenly and leaves a remainder 0. As the number 115 is a composite number, it has many factors other than 1 and 115. Therefore, the factors of 115 are 1, 5, 23 and 115. Similarly, the negative factors of 115 are -1, -5, -23 and -115.

 Factors of 115: 1, 5, 23 and 115. Prime Factorization of 115: 5 × 23.

Pair Factors of 115

The pair factors of 115 are the pair of numbers which are multiplied together and give the original number 115. Since 115 is a composite number, it has more than one pair factor. The following are the positive and negative pair factors of 115.

Positive Pair Factors of 115:

 Positive Factors of 115 Positive Pair Factors of 115 1 × 115 (1, 115) 5 × 23 (5, 23)

Therefore, the positive pair factors of 115 are (1, 115) and (5, 23).

Negative Pair Factors of 115:

 Negative Factors of 115 Negative Pair Factors of 115 -1 × -115 (-1, -115) -5 × -23 (-5, -23)

Hence, the negative pair factors of 115 are (-1, -115) and (-5, -23).

Factors of 115 by Division Method

The two different methods to find the factors of a number are the division method and the prime factorization method. Go through the following division method to find the factors of 115.

In the division method, the factors of 115 are found by dividing 115 by different integer numbers. If the integer divides 115 evenly and leaves a remainder 0, then the integer is a factor of 115. Now, let us start dividing 115 by 1 and continue with different integers.

• 115/1 = 115 (Factor = 1 and Remainder = 0)
• 115/5 = 23 (Factor = 5 and Remainder = 0)
• 115/23 = 5 (Factor = 23 and Remainder = 0)
• 115/115 = 1 (Factor = 115 and Remainder = 0)

If the number 115 is divisible by any numbers other than 1, 5, 23 and 115, it leaves a remainder value. Hence, the factors of 115 are 1, 5, 23 and 115.

Prime Factorization of 115

In the prime factorization of 115, the number 115 is written in the form of the product of its prime factors. Go through the prime factorization of 115 to find the prime factors of 115.

Consider a pair factor of 115, say (1, 115).

Here, the number 115 is a composite number that can be further divided into prime factors. Thus, the number 115 is written as the product of 5 and 23, where 5 and 23 are prime numbers

Hence, the prime factorization of 115 is 5 × 23.

Note: 1 is neither prime nor composite. So, leave the number 1, since it cannot be split further.

Solved Examples

Example 1:

Find the common factors of 115 and 116.

Solution:

The factors of 115 are 1, 5, 23 and 115.

The factors of 116 are 1, 2, 4, 29, 58 and 116.

Thus, the common factor of 115 and 116 is 1.

Example 2:

What are the common factors of 115 and 110?

Solution:

Factors of 115 = 1, 5, 23 and 115.

Factors of 110 = 1, 2, 5, 10, 11, 22, 55 and 110.

Hence, the common factors of 115 and 110 are 1 and 5.

Example 3:

Find the common factors of 115 and 46.

Solution:

The factors of 115 are 1, 5, 23 and 115.

The factors of 46 are 1, 2, 23 and 46.

Therefore, the common factors of 115 and 46 are 1 and 23.

Keep visiting BYJU’S – The Learning App and download the app to learn all the important Maths concepts in a fun way by exploring more videos.

Frequently Asked Questions on Factors of 115

What are the factors of 115?

The numbers that divide 115 completely without leaving a remainder are the factors of 115. As 115 is a composite number, it has more than two factors. Thus, the factors of 115 are 1, 5, 23 and 115.

What is the prime factorization of 115?

The prime factorization of 115 is 5 × 23 or 51 × 231.

What are the positive pair factors of 115?

The positive pair factors of 115 are (1, 115) and (5, 23).

What are the negative pair factors of 115?

The negative pair factors of 115 are (-1, -115) and (-5, -23)

Is 23 a factor of 115?

Yes, 23 is a factor of 115. As 23 divides 115 evenly and leaves a quotient value of 5 and remainder 0, 23 is a factor of 115.