Let’s work through this step by step.
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Section A, Question 1:
We’re given a 4x4 grid of numbers from 12 to 45 (part of a 100 square).
Shaded numbers:
→ 12, 15, 24, 33, 42, 45
Let’s list them:
12, 15, 24, 33, 42, 45
Check what they have in common:
- All are divisible by 3?
12 ÷ 3 = 4 → yes
15 ÷ 3 = 5 → yes
24 ÷ 3 = 8 → yes
33 ÷ 3 = 11 → yes
42 ÷ 3 = 14 → yes
45 ÷ 3 = 15 → yes
✔ So shaded numbers are all
multiples of 3
Circled numbers:
→ 12, 24, 32, 44
List: 12, 24, 32, 44
What do they have in common?
- Are they even? Yes — all end in even digits.
- Are they multiples of 4?
12 ÷ 4 = 3 → yes
24 ÷ 4 = 6 → yes
32 ÷ 4 = 8 → yes
44 ÷ 4 = 11 → yes
✔ So circled numbers are all
multiples of 4
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Section A, Question 2:
Grid from 55 to 90.
Shaded numbers:
→ 55, 60, 65, 70, 75, 80, 85, 90
List: 55, 60, 65, 70, 75, 80, 85, 90
What do they have in common?
All end in 0 or 5 → so they are all
multiples of 5
Check:
55 ÷ 5 = 11 → yes
60 ÷ 5 = 12 → yes
... up to 90 ÷ 5 = 18 → yes
✔
Circled numbers:
→ 55, 66, 77, 88
List: 55, 66, 77, 88
What do they have in common?
They are all multiples of 11:
55 = 11 × 5
66 = 11 × 6
77 = 11 × 7
88 = 11 × 8
✔
Also, they are palindromic (same forwards and backwards), but the math pattern here is clearly multiples of 11.
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Section B: Complete these sentences
Example:
3 is a
factor of 9; 9 is a
multiple of 3.
Now let’s fill in each:
1) 18 is a ___ of 3; 3 is a ___ of 18.
→ 18 ÷ 3 = 6 → so 18 is a
multiple of 3
→ 3 divides 18 → so 3 is a
factor of 18
Answer:
multiple,
factor
2) 4 and 5 are common ___ of 20; 20 is a ___ of 4 and 5.
→ 4 and 5 both divide 20 → so they are
factors of 20
→ 20 is a
multiple of both 4 and 5
Answer:
factors,
multiple
3) The highest common ___ of 18 and 30 is 6.
→ We’re talking about factors →
factor (HCF = Highest Common Factor)
Answer:
factor
4) 12 is a ___ of 24; 24 is a ___ of 12.
→ 12 divides 24 → 12 is a
factor of 24
→ 24 = 12 × 2 → 24 is a
multiple of 12
Answer:
factor,
multiple
5) The lowest common ___ of 4 and 10 is 20.
→ LCM = Lowest Common Multiple →
multiple
Answer:
multiple
6) 1 is a ___ of every number.
→ 1 divides every whole number →
factor
Answer:
factor
7) 0 is a ___ of every number.
→ This is tricky. Actually, 0 is a
multiple of every number, because any number × 0 = 0.
So: 0 = 5 × 0 → 0 is a multiple of 5
Answer:
multiple
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Final Answers:
Section A:
1)
Shaded numbers: multiples of 3
Circled numbers: multiples of 4
2)
Shaded numbers: multiples of 5
Circled numbers: multiples of 11
Section B:
1) multiple, factor
2) factors, multiple
3) factor
4) factor, multiple
5) multiple
6) factor
7) multiple
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Final Answer:
Section A1: Shaded — multiples of 3; Circled — multiples of 4
Section A2: Shaded — multiples of 5; Circled — multiples of 11
Section B1: multiple, factor
Section B2: factors, multiple
Section B3: factor
Section B4: factor, multiple
Section B5: multiple
Section B6: factor
Section B7: multiple
Parent Tip: Review the logic above to help your child master the concept of math worksheet for factors and multiples.
