Factors of 82

82 is the number that can be expressed as a sum of 3 prime numbers as 2 + 19 + 61. 82 is a composite number. In this lesson, we will calculate the factors of 82, prime factors of 82, and factors of 82 in pairs along with solved examples for a better understanding. 

• Factors of 82: 1, 2, 41 and 82.
• Prime Factorization of 82: 2 × 41

The integers that completely divide 82 leaving without any remainder are the factors of 82. They are 1, 2, 41 and 82.

• 82 is divisible by 1 and itself. 
• Using the divisibility rules, perform the divisibility tests on all the integers starting from 2 upto 41(half of 82)
• We find that 82 ÷ 2 = 41 and 82 ÷ 41 = 2
• With no other integer 82 is divisible.

To understand the concept of finding factors by prime factorization better, let us take a few more examples.

• Factors of 83: The factors of 83 are 1 and 83.
• Factors of 81: The factors of 81 are 1, 3, 9, 27 and 81.
• Factors of 94: The factors of 94 are 1, 2, 47 and 94.
• Factors of 84:The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 26, 28, 42, and 84.
• Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

Prime factorization is to express a composite number as the product of its prime factors. 

• Divide 82 by the smallest prime number 2, being it even. 81 ÷ 2 = 41
• We cannot factorize 41 as it is a prime number itself.
• Using the division method, we determine the prime factors are 2 and 41. 

The numbers that give the product of 82 when multiplied together in pairs are the factors of 82 in pairs. 

• 1 × 82 = 82 and -1 × -82 = 82
• 2 × 41 = 82 and -2 × -41 = 82
• 41  × 2 = 82 and -41 × -2 = 82
• 82 × 1= 82 and -82 × -1 = 82

Thus the factors of 82 in pairs are (1, 82), (-1, -82), (2, 41)and (-2, -41)

• The prime factorization of 82 = 2 × 41
• The exponents of each of these factors = 1, i.e. 2¹ × 41¹
• Add 1 to each and multiply them. (1+1) × (1+1) = 2 × 2 = 4
• Thus we conclude that there are only 4 factors of 82. 

• The factors of 82 are 1, 2, 41 and 82
• The prime factors of 82 are 2 and 41.
• The distinct factors of 82 in pairs are (1, 82) and (2, 41)

What are the factors of 82?

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

What are the common factors of 82 and 81?

The factors of 82 are 1, 2, 41 and 82.
The factors of 81 are 1, 3, 27 and 81.
The common factor of 82 and 81 is 1.

What are the factors of 82 that sum up to 84?

The factors of 82 are 1, 2, 41 and 82. 82 + 2 = 84.

What are the prime factors of 82?

2 and 41 are the prime factors of 82.

What do the factors of 82 sum up to?

The factors of 82 are 1, 2, 41 and 82. Their sum = 1 + 2 + 41 + 82 = 126