Identify Factors and Multiples
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What you will learn
- 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
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 whole number greater than 1 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, 2, 3, 4, 6, and 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).
Words to know
Factor
A number that divides evenly into another number, leaving no remainder
e.g. 3 is a factor of 12 because 12 ÷ 3 = 4.
Factor pair
Two factors that multiply to give the original number
e.g. (2, 6) is a factor pair of 12.
Multiple
The product of a number and any whole number
e.g. 15 is a multiple of 5.
Divisible
When one number can be divided exactly by another with no remainder
e.g. 24 is divisible by 6.
Product
The result of multiplying two or more numbers
e.g. The product of 4 and 5 is 20.
Tip: to find all factor pairs of a number, divide it by 1, 2, 3, 4, and so on. Stop when the quotient is smaller than the divisor — you have found all pairs.
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