Factor Calculator

Factors of 82

The factors of 82 are 1, 2, 41, and 82. In total, 82 has 4 factors. Its prime factorization is 2 × 41, and the sum of all its factors is 126.

All factors of 82

Here are all 4 factors of 82, listed from smallest to largest.

124182

Factor pairs of 82

These 2 pairs of whole numbers each multiply to give 82.

1 × 82 = 82
2 × 41 = 82

Prime factorization of 82

Dividing 82 by the smallest prime at each step gives its prime factorization:

82 ÷ 2 = 41
41 ÷ 41 = 1
Result: 82 = 2 × 41 = 2 × 41

The distinct prime factors of 82 are 2, 41. To factorize any other number, use the prime factorization calculator.

Factor tree of 82

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 8282241
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 82

Number of factors4
Sum of factors126
Sum of proper factors44
Prime factorization2 × 41
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 82 interesting

  • 82 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 82 is a deficient number: its proper factors sum to 44, which is 38 less than 82 itself.

How to find the factors of 82 yourself

Divide 82 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √82 ≈ 9.06, because every factor above that pairs with one below it.

82 ÷ 1 = 82 ✓
82 ÷ 2 = 41 ✓

Reading both columns gives every factor: 1, 2, 41, 82. The factor calculator does this automatically for any number.

Numbers mathematically connected to 82.

Frequently asked questions about 82

What are the factors of 82?

The factors of 82 are 1, 2, 41, and 82. That is 4 factors in total, counting both 1 and 82.

Is 82 a prime number?

No, 82 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 82 is also divisible by 2.

What is the prime factorization of 82?

The prime factorization of 82 is 2 × 41. Written out in full: 2 × 41 = 82. Its distinct prime factors are 2, 41.

What two numbers multiply to give 82?

There are 2 pairs of whole numbers that multiply to 82: 1 × 82, 2 × 41.

What is the sum of the factors of 82?

Adding all the factors of 82 together gives 126. Excluding 82 itself, the proper factors sum to 44.

Is 82 a perfect square?

No, 82 is not a perfect square. There is no whole number that multiplies by itself to give 82. The nearest perfect squares are 81 and 100.

What is the largest factor of 82 other than itself?

The largest factor of 82 apart from 82 itself is 41, since 82 ÷ 41 = 2.

How many factors does 82 have?

82 has 4 factors: 1, 2, 41, and 82. You can verify this from the prime factorization 2 × 41: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 82 down further with the prime factorization calculator, or compare 82 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.