🔢 MathGrade 4Lesson 5
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Identify Factors and Multiples

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 1Define factors as numbers that divide evenly into a given number
  • 2List all factor pairs for numbers up to 50
  • 3Define multiples as products of a number and any whole number
  • 4Distinguish between factors and multiples of a given number
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Mini Lesson

Factors and multiples are two key ideas in number theory. A factor divides evenly into a number with no remainder. A multiple is what you get when you multiply a number by 1, 2, 3, and so on. Understanding both helps with fractions, common denominators, and problem solving.

What Is a Factor?

  • A factor is a number that divides evenly into another number (no remainder left over).
  • Example: 12 ÷ 3 = 4 with no remainder, so 3 is a factor of 12.
  • Every number has at least two factors: 1 and itself.
  • Factor pairs for 12: (1, 12), (2, 6), (3, 4) — each pair multiplies to give 12.

What Is a Multiple?

  • A multiple is the result of multiplying a number by any whole number (1, 2, 3, ...).
  • Multiples of 5: 5, 10, 15, 20, 25, 30, ... — the list never ends.
  • A number always has infinitely many multiples.
  • To check: is 35 a multiple of 7? Yes, because 7 × 5 = 35.

Key Difference

  • Factors are smaller than or equal to the number (factors of 12 are 1 through 12).
  • Multiples are greater than or equal to the number (multiples of 12: 12, 24, 36, ...).
  • Divisible means a number can be divided evenly: 18 is divisible by 6 (18 ÷ 6 = 3).
Factor pairs chart for 12Factor Pairs of 12Factor 1xFactor 21x122x63x4Each pair multiplies to 12
Multiples of 5 on a number lineMultiples of 5051015202530+5+5+5+5+5+55, 10, 15, 20, 25, 30 ... (goes on forever)Skip-count by 5 to list multiples of 5.
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Tip: to find all factors of a number, start at 1 and try dividing by 2, 3, 4, ... up to the number itself. Stop when the quotient is smaller than the divisor — you have found all pairs.

Vocabulary
Factor
A number that divides evenly into another number, leaving no remaindere.g. 3 is a factor of 12 because 12 ÷ 3 = 4.
Factor pair
Two factors that multiply to give the original numbere.g. (2, 6) is a factor pair of 12.
Multiple
The product of a number and any whole numbere.g. 15 is a multiple of 5.
Divisible
When one number can be divided exactly by another with no remaindere.g. 24 is divisible by 6.
Product
The result of multiplying two or more numberse.g. The product of 4 and 5 is 20.
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