Factors and Multiples

Grade 4 · Math · Study Guide

Explore how numbers relate to each other through factors, multiples, and divisibility.

A factor is a number that divides evenly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. You can think of factors as pairs of numbers you multiply together to get the original number: 1 × 12, 2 × 6, and 3 × 4 all equal 12.

A multiple is the result of multiplying a number by any whole number. Multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. Every number is a multiple of itself and also a multiple of 1.

A prime number has exactly two factors: 1 and itself. Examples include 2, 3, 5, 7, 11, and 13. A composite number has more than two factors. The number 1 is neither prime nor composite.

Common factors are factors that two numbers share. The greatest common factor (GCF) is the largest one they share. Common multiples are multiples that two numbers share. The least common multiple (LCM) is the smallest one they share. These ideas are useful for working with fractions.

Key terms

Factor
A whole number that divides evenly into another number.
Multiple
The result of multiplying a number by a whole number; skip counting gives multiples.
Prime number
A whole number greater than 1 that has exactly two factors: 1 and itself.
Composite number
A whole number greater than 1 that has more than two factors.
Greatest Common Factor (GCF)
The largest factor that two or more numbers share.
Least Common Multiple (LCM)
The smallest multiple that two or more numbers share.

Flashcards

Factors of 18
1, 2, 3, 6, 9, 18 — these are all the numbers that divide evenly into 18
Multiples of 7
7, 14, 21, 28, 35, 42 ... (multiply 7 by 1, 2, 3, 4 ...)
Prime number
Has exactly 2 factors: 1 and itself; examples: 2, 3, 5, 7, 11, 13, 17, 19
Composite number
Has more than 2 factors; examples: 4, 6, 8, 9, 10, 12
GCF of 12 and 16
4 — factors of 12: 1,2,3,4,6,12; factors of 16: 1,2,4,8,16; largest shared is 4
LCM of 4 and 6
12 — multiples of 4: 4,8,12; multiples of 6: 6,12; smallest shared is 12
Factor pairs of 20
1 × 20, 2 × 10, 4 × 5 — three pairs of factors that multiply to give 20
Is every even number composite?
Almost — except 2, which is the only even prime number; all other even numbers have at least 3 factors

Questions

  1. Which of the following is a factor of 24?

    1. 5
    2. 7
    3. 8
    4. 9
    Show answer

    Answer: 8

    24 ÷ 8 = 3 with no remainder, so 8 is a factor of 24. Check: 5, 7, and 9 do not divide evenly into 24.

  2. The number 17 is a prime number.

    Show answer

    Answer: True

    17 has only two factors: 1 and 17. No other whole number divides evenly into it, so it is prime.

  3. The GCF of 8 and 12 is _____.

    Show answer

    Answer: 4

    Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. The greatest factor they share is 4.

  4. Which list shows the first four multiples of 6?

    1. 1, 2, 3, 6
    2. 6, 12, 14, 18
    3. 6, 12, 18, 24
    4. 2, 4, 6, 12
    Show answer

    Answer: 6, 12, 18, 24

    Multiples of 6: 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, 6 × 4 = 24. Option C is 6, 12, 18, 24.

  5. The number 1 is considered a prime number.

    Show answer

    Answer: False

    The number 1 has only one factor (itself). Prime numbers must have exactly two factors. So 1 is neither prime nor composite.

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