BYTETOOLS

Factors Calculator

List every factor of a number with factor pairs, count and sum. Flags primes and perfect, abundant or deficient numbers instantly in your browser.

6
Factors
56
Sum of factors
No
Prime?
Perfect
Type

All factors of 28

1, 2, 4, 7, 14, 28

Factor pairs

1 × 282 × 144 × 7

Sum of proper factors (excluding 28 itself): 28 — equal to the number, so it is a perfect number.

What is the Factors Calculator?

The ByteTools Factors Calculator lists every factor of a whole number, groups them into factor pairs, and reports the count and sum.

  • Complete list of factors, always in order
  • Factor pairs shown as multiplications
  • Count, sum and proper-factor sum
  • Prime, perfect, abundant and deficient classification
  • Handles numbers up to one trillion via √n trial division
  • 100% private — runs entirely in your browser

How to use the Factors Calculator

  1. 1

    Enter a positive whole number (up to 1,000,000,000,000).

  2. 2

    Read the complete factor list and the factor pairs.

  3. 3

    Check the count, sum, and prime / perfect / abundant / deficient flags.

  4. 4

    Copy the factor list with one click.

About the Factors Calculator

The ByteTools Factors Calculator lists every factor of a whole number, groups them into factor pairs, and reports the count and sum. It finds factors by trial division up to the square root — every divisor i below the root pairs with n ÷ i above it, which is why the pairs view is both fast and complete.

Beyond the list, it classifies the number: prime or composite, and perfect, abundant or deficient based on the sum of its proper factors. 28 is perfect because 1 + 2 + 4 + 7 + 14 = 28, while 12 is abundant and 10 is deficient. Handy for homework, number theory practice and puzzle solving.

Numbers up to one trillion are supported, and everything is computed instantly and locally in your browser. Nothing is uploaded, and you can copy the full factor list with one click.

Frequently asked questions

What are the factors of a number?

Factors are the whole numbers that divide it exactly, with no remainder. The factors of 28 are 1, 2, 4, 7, 14 and 28. Every number has at least two factors (1 and itself) unless it is 1, which has only one.

How do you find all factors of a number quickly?

Test divisors only up to the square root. Every divisor found below √n automatically pairs with one above it: for 28, finding 2 also gives you 14. This is why the calculator can factor a trillion-sized number instantly — it needs at most a million trial divisions.

What is a factor pair?

Two numbers that multiply to give the original number. The factor pairs of 28 are 1 × 28, 2 × 14 and 4 × 7. A perfect square like 36 has one 'pair' where both members are equal: 6 × 6.

What is a perfect number?

A number that equals the sum of its proper factors (all factors except itself). 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14 are the two smallest. If the proper-factor sum is bigger the number is abundant; if smaller, deficient.

What is the difference between factors and prime factors?

Factors are all divisors of a number; prime factors are only the prime ones, usually written as a product of powers. The factors of 12 are 1, 2, 3, 4, 6, 12, while its prime factorization is 2² × 3. Use our Prime Factorization tool for the latter.

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