Skill: Identify factors of a number

Explanation and Free Practice Resources

Factors are the positive whole numbers that divide a given whole number evenly, so the quotient is also a whole number; equivalently, they form complete factor pairs whose product is the number, including 1 and the number itself. This understanding applies especially to whole numbers within 100, distinguishes factors from multiples, and supports recognizing prime numbers; negative, fractional, and algebraic factors are beyond this scope.

Detailed Explanation: Identify factors of a number

Factors are positive whole numbers that divide a number evenly, with no remainder. Factors always come in pairs that multiply to make the given number.

Example: Find all the factors of 2424.

Start with 11:

  • 1×24=241 \times 24 = 24, so 11 and 2424 are factors.

Try the next numbers:

  • 2×12=242 \times 12 = 24, so 22 and 1212 are factors.
  • 3×8=243 \times 8 = 24, so 33 and 88 are factors.
  • 4×6=244 \times 6 = 24, so 44 and 66 are factors.
  • 55 does not divide 2424 evenly, so it is not a factor.

The factor pairs are:

1×24,2×12,3×8,4×61 \times 24,\quad 2 \times 12,\quad 3 \times 8,\quad 4 \times 6

So, the factors of 2424 are:

1,2,3,4,6,8,12,24\boxed{1, 2, 3, 4, 6, 8, 12, 24}

Remember: factors divide evenly into a number. Multiples are the numbers you get when you multiply a number by 1,2,3,…1, 2, 3,\ldots

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Division Dividend to Factor Pair - 2 Digit


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