Factor — Grade 6 Math, what it means and where it is taught
A number that divides evenly into another.
Taught in Grade 6 Math.
Where it is taught
What uses it later
This idea is needed for:
- GCF — Greatest common factor — the largest number dividing both.
- Prime polynomial — One that will not factor any further over the integers.
- Simplest radical form — No perfect square factors left under the root.
- Factor theorem — If f(a) = 0 then x - a is a factor, and the other way round.
Practise this idea
71 questions in the course bank use Factor, in Positive Rational Number Operations, Proportional Reasoning with Scale Drawings, GCF and LCM, Measurement, Dilations & Similarity, Scatter Plots & Association. The first 8 are below; the rest are in those units.
Problem 1
Which of these fractions gives a decimal that terminates (stops)?
- 712
- 56
- 940
- 415
Worked answer
940
40 = 23 × 5 — only 2s and 5s, so it terminates (940 = 0.225)
12, 6 and 15 each contain a factor of 3, so those repeat.
Problem 2
A 4 in by 6 in photo is enlarged by factor 3. How long is the longer side now?
Worked answer
18
6 × 3 = 18 in
Problem 3
A 3 × 4 rectangle is scaled by factor 2. Find the new area.
Worked answer
48
New rectangle: 6 × 8 = 48
Check: original area 12, times 22 = 4, gives 48 ✓
Problem 4
If every length is multiplied by 4, the area is multiplied by what?
- 4
- 8
- 16
- 64
Worked answer
16
k2 = 42 = 16
Problem 5
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 6
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 7
Find the LCM of 5 and 7.
Worked answer
35
5 and 7 are relatively prime
LCM = 5 × 7 = 35
Problem 8
How many square centimetres are in 1 square metre?
Worked answer
10000
1 m2 is 100 cm × 100 cm
= 10,000 cm2