GCF — Grade 6 Math, what it means and where it is taught
Greatest common factor — the largest number dividing both.
Taught in Grade 6 Math.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Factor — A number that divides evenly into another.
Practise this idea
13 questions in the course bank use GCF, in GCF and LCM, Expressions, Structure & Units, Factoring. The first 8 are below; the rest are in those units.
Problem 1
Find the GCF of 12 and 18.
Worked answer
6
Factors of 12: 1,2,3,4,6,12
Factors of 18: 1,2,3,6,9,18
Largest shared: 6
Problem 2
Find the GCF of 8 and 15.
Worked answer
1
8 = 23 and 15 = 3 · 5
No shared primes, so the GCF is 1 — they are relatively prime.
Problem 3
Find the GCF of 24 and 36.
Worked answer
12
24 = 23 · 3, 36 = 22 · 32
Shared at lowest powers: 22 · 3
= 12
Problem 4
Find the GCF of 18 and 30.
Worked answer
6
18 = 2 · 32, 30 = 2 · 3 · 5
Shared: 2 · 3 = 6
Problem 5
A florist has 48 roses and 36 tulips and wants identical bunches using every flower. What is the greatest number of bunches?
Worked answer
12
48 = 24 · 3, 36 = 22 · 32
GCF = 22 · 3 = 12
Each bunch: 4 roses and 3 tulips.
Problem 6
Two numbers have GCF 6 and LCM 90. One of them is 18. Find the other.
Worked answer
30
6 × 90 = 540
540 ÷ 18 = 30
Check: GCF(18, 30) = 6 ✓
Problem 7
Find the GCF of 84 and 126.
Worked answer
42
84 = 22 · 3 · 7
126 = 2 · 32 · 7
Shared at lowest powers: 2 · 3 · 7 = 42
Problem 8
Two numbers have GCF 8 and LCM 48. One is 16. Find the other.
Worked answer
24
8 × 48 = 384
384 ÷ 16 = 24