1. Steps to find factors of 82 using Division Method

Example: Find factors of 82

  • Divide 82 by 1: 82 ÷ 1 : Remainder = 0
  • Divide 82 by 2: 82 ÷ 2 : Remainder = 0
  • Divide 82 by 41: 82 ÷ 41 : Remainder = 0
  • Divide 82 by 82: 82 ÷ 82 : Remainder = 0

Hence, Factors of 82 are 1, 2, 41, and 82

2. Steps to find factors of 82 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 82 using the division method, follow these steps:

  • Step 1. Start dividing 82 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 82, which is 2. Divide 82 by 2 to obtain the quotient (41).
    82 ÷ 2 = 41
  • Step 3. Repeat step 1 with the obtained quotient (41).
    41 ÷ 41 = 1

So, the prime factorization of 82 is, 82 = 2 x 41.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 82 as shown below:

So, the prime factorization of 82 is, 82 = 2 x 41.

3. Find factors of 82 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 82 would be the two numbers which, when multiplied, give 82 as the result.

The following table represents the calculation of factors of 82 in pairs:

Factor Pair Pair Factorization
1 and 82 1 x 82 = 82
2 and 41 2 x 41 = 82

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 82. They are called negative pair factors.

Hence, the negative pairs of 82 would be ( -1 , -82 ) , ( -2 , -41 ) .

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 82 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 41, 82 are exact divisors of 82.
  • 1 is a factor of every number. Eg. 1 is a factor of 82.
  • Every number is a factor of zero (0), since 82 x 0 = 0.

Frequently Asked Questions

  • What are the prime factors of 82?

    The factors of 82 are 1, 2, 41, 82.
    Prime factors of 82 are 2, 41.

  • What is the sum of all factors of 82?

    The sum of all factors of 82 is 126.

  • What are the pair factors of 82?

    Pair factors of 82 are (1,82), (2,41).

  • What two numbers make 82?

    Two numbers that make 82 are 2 and 41.

  • What are multiples of 82?

    First five multiples of 82 are 164, 246, 328, 410.

  • Is 82 a perfect square?

    No 82 is not a perfect square.

  • Which is greatest factor of 82?

    The greatest factor of 82 is 41.

  • How do you factors of 82?

    Factors of 82 are 1, 2, 41, 82.

  • What are five multiples of 82?

    First five multiples of 82 are 164, 246, 328, 410, 492.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 82?

Factors of 82 are 1, 2, 41, 82.
Even factors of 82 are 2, 82.
Hence, product of even factors of 82 is; 2 x 82 = 164.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 82? Help her in writing all the factors.

Positive factors are 1, 2, 41, 82.
Negative factors are -1, -2, -41, -82.

How many factors are there for 82?

Factors of 82 are 1, 2, 41, 82.
So there are in total 4 factors.

Sammy is puzzled while calculating the prime factors of 82. Can you help him find them?

Factors of 82 are 1, 2, 41, 82.
Prime factors of 82 are 2, 41

Joey wants to write all the prime factors of 82 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 82 are 2, 41.
So in exponential form it can be written as 2 x 41.

What is prime factorization of 82?

Prime factorization of 82 is 2 x 41 = 2 x 41.

Can you help Rubel to find out the product of the even factors of 82?

Factors of 82 are 1, 2, 41, 82.
Even factors of 82 are 2, 82.
Hence, product of even factors of 82 is; 2 x 82 = 164.