What is the difference between a factor and a multiple?

A factor divides evenly into a number; a multiple is what you get when you multiply the number by an integer. The factors of 12 are 1, 2, 3, 4, 6, and 12. The multiples of 12 are 12, 24, 36, 48, and so on — factors stop at the number, multiples go on forever.

How do you know when you have found every factor?

Check divisors only up to the square root of the number. Every factor larger than the square root pairs with a smaller one you already found, so nothing new appears past that point. For 28, √28 ≈ 5.29, so testing 1 through 5 finds all three pairs: (1, 28), (2, 14), and (4, 7).

Is 1 a factor of every whole number?

Yes — 1 divides every whole number evenly, so it opens every factor list. It is also the only factor that 1 itself has, which is why 1 is neither prime nor composite.

Does the order of factors matter?

No — this calculator lists factors in ascending order by convention, but 28 has the same six factors no matter how you arrange them: 1, 2, 4, 7, 14, and 28.

Factor Calculator

List every factor of any whole number in ascending order, with factor pairs, factor count, a prime check, and a visual pair chart. Results update instantly. Free, no sign-up.

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How Factoring Works

A factor is a whole number that divides another with nothing left over. To find them all, you only need to test divisors up to the square root: every factor below √n pairs with one above it. For 28, testing 1–5 finds 1, 2, 4 — and their partners 28, 14, 7 fall out automatically.

Numbers with exactly two factors are prime. Numbers like 28, whose proper factors (1 + 2 + 4 + 7 + 14) add up to the number itself, are called perfect — only 51 are known, and they connect to some of the largest prime numbers ever found.

Where Factors Show Up

Simplifying fractions, finding common denominators, splitting bills evenly, tiling a floor with no cuts, and scheduling repeating events all lean on factors. In cryptography, the fact that factoring huge numbers is hard is what keeps RSA encryption — and much of the internet — secure.

Frequently Asked Questions

What are the factors of 28?

1, 2, 4, 7, 14, and 28 — six factors in three pairs: 1×28, 2×14, 4×7.

What is the difference between factors and multiples?

Factors divide into a number (factors of 12: 1, 2, 3, 4, 6, 12); multiples are what you get multiplying outward (12, 24, 36, …).

How do you know if a number is prime?

It has exactly two factors: 1 and itself. This calculator flags primes automatically.

What are factor pairs?

Two numbers that multiply to give the original — e.g. 4 × 7 = 28, so (4, 7) is a factor pair of 28.

What is a perfect number?

A number equal to the sum of its proper factors. 28 is perfect: 1+2+4+7+14 = 28. The next is 496.

Factor Calculator

How Factoring Works

Where Factors Show Up

Frequently Asked Questions

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