Math explorers

Factors & Multiples

Grade 6Number Theory

Use prime factorization to find greatest common factors and least common multiples.

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1Factors and prime numbers

Factors divide a number exactly. A prime has exactly two positive factors: 1 and itself. The number 1 is not prime.

Worked exampleFactors of 12: 1, 2, 3, 4, 6, 12

Multiples of 12 are 12, 24, 36, 48, … . Factors divide into a number; multiples are products of it.

Split a composite number into factors until every factor is prime. A factor tree helps organize the steps.

Worked example24 = 4 × 6 = 2 × 2 × 2 × 3

60 = 2 × 2 × 3 × 5. Check your factorization by multiplying all the prime factors.

For GCF, multiply the prime factors shared by both numbers, using the smaller count of each prime.

Worked example36 = 2² × 3²; 48 = 2⁴ × 3

GCF = 2² × 3 = 12. This gives the greatest number of identical groups when sharing 36 and 48 items with none left.

For LCM, include every prime factor needed by either number, using the larger count of each prime.

Worked example12 = 2² × 3; 18 = 2 × 3²

LCM = 2² × 3² = 36. Events repeating every 12 and 18 minutes next happen together after 36 minutes.

Question 1 of 5

Which is the prime factorization of 30?

Need a hint?

Every factor must be prime.