Multiples and factors (prime factorization)

Practice 3 items →

Prime factorization is the canonical name of a number. GCF is the shared primes at their lowest powers; LCM is all primes at their highest powers. Students use factor trees and continuous division, write index notation, and solve tiling (GCF) and repeating-cycle (LCM) stories.

Specification · for a parent or teacher
Part no.
prime-factorization-gcf-lcm
Course
Advanced Math 5 · Unit 3
Realm
Numbers
Difficulty
3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty
3 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

factor trees and continuous division; index notation 23×32×52^3 \times 3^2 \times 5; GCF and LCM from primes; tiling (GCF) and repeating-cycle (LCM) stories.

Ready when

GCF and LCM of 24 and 90 from 24=23⋅324=2^3\cdot 3 and 90=2⋅32⋅590=2\cdot 3^2\cdot 5, no listing.

Formulas

GCF from primes
GCF(2a3b, 2c3d)=2min⁡(a,c)3min⁡(b,d)\text{GCF}(2^a 3^b,\ 2^c 3^d) = 2^{\min(a,c)}3^{\min(b,d)}
LCM from primes
LCM(2a3b, 2c3d)=2max⁡(a,c)3max⁡(b,d)\text{LCM}(2^a 3^b,\ 2^c 3^d) = 2^{\max(a,c)}3^{\max(b,d)}

Watch for

LCM of 8 and 12 as 24 vs 96 (missing vs extra factors); GCF of 8 and 12 as 2.

Before · requires

After · used by

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prime-factorization-gcf-lcm

Items: prime-factorization-gcf-lcm-01 · prime-factorization-gcf-lcm-02 · prime-factorization-gcf-lcm-03