Factors of 65

The factors of 65 will be 1, 5, 13, and 65. These are the only numbers which divide 65 evenly without leaving any remainder. And, it always will be in a whole number. These are the only numbers that divide 65 exactly.

Negative Factors of 65 : Negative Factors of 65 are 1, 5, 13, and 65.

Prime Factors of 65: 5 and 13

Prime Factorization of 65:  It is expressed as 5×13

The Sum of Factors of 65:  The sum of factors of 65 is 1 + 5 + 13 + 65 =84
 

To find the factors of 65, students need to divide the original number evenly without leaving a remainder. Some methods are explained below for easy solution of factors-

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization

• Factor Tree

Students need to find pairs of numbers that multiply together to give the original number.

Step 1: Check number from 2 up to the square root of the number.

Step 2: To each number, find its pair.

1×65 =65

5×13 =65

6, 7 do not divide 65 evenly.

Therefore, the factors of 65 are 1, 5, 13, and 65.

This method is a process of systematically multiplying different numbers to get the original number.
 

If children get the division in a whole number, then both the divisor and the quotient are factors.

Check numbers from 2 up to the square root of 65, where the square root of 65 is ±8.06. So, you need to check until 8.

65 / 1 = 65, both 1 and 65 are factors.

65 / 5 = 13, both 5 and 13 are factors

65 / 6, 7, 8 won’t result in whole number.

Then, the factors of 65 will be 1, 5, 13, and 65.
 

Prime factors are the numbers that divide a given number evenly without a remainder. And, prime factorization is the process of breaking down a number into its prime factors.

Prime Factors of 65 = 5 and 13

Prime Factorization of 65 = 5×13
 

A factor tree is a visual representation of the prime factorization of a number.

= 5 and 15 are the prime building blocks of 65.

Factor Pairs: A factor pair is a combination of two numbers that multiply together to result in a specific value.

Factor a pair of number of 65 = 1 and 65 = 1×65 =65
                                                = 5 and 13 = 5×13 =65

The above numbers are the factor pair for 65, as 65 only holds a few divisors.

Positive Pair Factors =1 and, 65, 5 and 13

Negative Pair Factors = -1 and -65, -5 and -13

• Factor:This is a number that divides another number evenly without leaving any remainder.

• Divisor:It is said to be a number that divides another number evenly without leaving a remainder.

• Composite Number :A number which is greater than 1, and it has at least one positive integer other than 1 and the number itself.

• Multiple: It is a product of the given number and some other integer.