1. Steps to find factors of 65 using Division Method

Example: Find factors of 65

  • Divide 65 by 1: 65 ÷ 1 : Remainder = 0
  • Divide 65 by 5: 65 ÷ 5 : Remainder = 0
  • Divide 65 by 13: 65 ÷ 13 : Remainder = 0
  • Divide 65 by 65: 65 ÷ 65 : Remainder = 0

Hence, Factors of 65 are 1, 5, 13, and 65

2. Steps to find factors of 65 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 65 using the division method, follow these steps:

  • Step 1. Start dividing 65 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 65, which is 5. Divide 65 by 5 to obtain the quotient (13).
    65 ÷ 5 = 13
  • Step 3. Repeat step 1 with the obtained quotient (13).
    13 ÷ 13 = 1

So, the prime factorization of 65 is, 65 = 5 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 65 as shown below:

So, the prime factorization of 65 is, 65 = 5 x 13.

3. Find factors of 65 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 65 would be the two numbers which, when multiplied, give 65 as the result.

The following table represents the calculation of factors of 65 in pairs:

Factor Pair Pair Factorization
1 and 65 1 x 65 = 65
5 and 13 5 x 13 = 65

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 65. They are called negative pair factors.

Hence, the negative pairs of 65 would be ( -1 , -65 ) , ( -5 , -13 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Every factor of a number is an exact divisor of that number, example 1, 5, 13, 65 are exact divisors of 65.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 65 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 65.

Frequently Asked Questions

  • What two numbers make 65?

    Two numbers that make 65 are 5 and 13.

  • What is prime factorization of 65?

    Prime factorization of 65 is 5 x 13.

  • Write some multiples of 65?

    First five multiples of 65 are 130, 195, 260, 325.

  • Which is the smallest prime factor of 65?

    The smallest prime factor of 65 is 5.

  • Is 65 a perfect square?

    No 65 is not a perfect square.

  • What is the sum of all factors of 65?

    The sum of all factors of 65 is 84.

  • What are factors of 65?

    Factors of 65 are 1, 5, 13, 65.

  • How do you find factors of a negative number? ( eg. -65 )?

    Factors of -65 are -1, -5, -13, -65.

  • Is 65 a whole number?

    Yes 65 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 65. Help him in finding the mean of 65.

Factors of 65 are 1, 5, 13, 65.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 65 is 1 + 5 + 13 + 65 = 84.
Hence, the mean of factors of 65 is 84 ÷ 4 = 21.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 65? Help her in writing all the factors.

Positive factors are 1, 5, 13, 65.
Negative factors are -1, -5, -13, -65.

Joey wants to write all the prime factors of 65 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 65 are 5, 13.
So in exponential form it can be written as 5 x 13.

Kevin has been asked to write 3 factor(s) of 65. Can you predict the answer?

3 factor(s) of 65 are 1, 5, 13.

Sammy is puzzled while calculating the prime factors of 65. Can you help him find them?

Factors of 65 are 1, 5, 13, 65.
Prime factors of 65 are 5, 13

What is prime factorization of 65?

Prime factorization of 65 is 5 x 13 = 5 x 13.

Can you help Rubel to find out the product of the even factors of 65?

Factors of 65 are 1, 5, 13, 65.
Even factors of 65 are 0.
Hence, product of even factors of 65 is; 0 = 0.