Question Hidden box (a)
Which multipliers can produce all four outputs 28, 36, 48 and 72?
Steps only
CLASS 5 · MATHS MELA · CHAPTER 13
Animal Jumps
Use arrays and jumps to understand factors, multiples, common factors, common multiples and divisibility.
62 worked answersAll 4 exercise setsAll 11 end-of-chapter questions
What you will learn
- Find factors with rectangular arrays.
- Identify common factors and common multiples.
- Apply divisibility ideas to trails, schedules and number sorting.
62 worked answers · short steps first, explanations when you need them
Factors and Rectangular Arrays
Textbook pages 164–165
Question 15 arrays
Make all rectangular arrays for 15.
Steps only
15=1×15=3×5.
Answer
The factor pairs are 1×15 and 3×5; factors are 1, 3, 5 and 15.
Question 12 blanks
Complete 2×__=12, 3×__=12, 12×__=12 and 1×__=12.
Steps only
12÷2=6; 12÷3=4; 12÷12=1; 12÷1=12.
Answer
6, 4, 1 and 12, respectively.
Question Arrays a
Make arrays for 10 and list its factors.
Steps only
10=1×10, 2×5.
Answer
Factors: 1, 2, 5, 10.
Question Arrays b
Make arrays for 14 and list its factors.
Steps only
14=1×14, 2×7.
Answer
Factors: 1, 2, 7, 14.
Question Arrays c
Make arrays for 13 and list its factors.
Steps only
13=1×13.
Answer
Factors: 1, 13.
Question Arrays d
Make arrays for 20 and list its factors.
Steps only
20=1×20, 2×10, 4×5.
Answer
Factors: 1, 2, 4, 5, 10, 20.
Question Arrays e
Make arrays for 25 and list its factors.
Steps only
25=1×25, 5×5.
Answer
Factors: 1, 5, 25.
Question Arrays f
Make arrays for 32 and list its factors.
Steps only
32=1×32, 2×16, 4×8.
Answer
Factors: 1, 2, 4, 8, 16, 32.
Question Arrays g
Make arrays for 37 and list its factors.
Steps only
37=1×37.
Answer
Factors: 1, 37.
Question Arrays h
Make arrays for 46 and list its factors.
Steps only
46=1×46, 2×23.
Answer
Factors: 1, 2, 23, 46.
Question Arrays i
Make arrays for 54 and list its factors.
Steps only
54=1×54, 2×27, 3×18, 6×9.
Answer
Factors: 1, 2, 3, 6, 9, 18, 27, 54.
Question Prime observation
Why are 13 and 37 prime?
Steps only
Each has only the array 1×itself.
Answer
Each has exactly two factors: 1 and itself.
Animal Jumps and Common Multiples
Textbook pages 165–167
Question Rabbit and frog
A rabbit jumps by 4 and a frog by 3. Which numbers do both touch?
Steps only
Multiples of 3 and 4 first meet at 12.
Continue by adding 12.
Answer
12, 24, 36, 48, 60, …
Question Spider and grasshopper
Find common multiples of jumps 3 and 6.
Steps only
Every multiple of 6 is also a multiple of 3.
Answer
6, 12, 18, 24, 30, …
Question 4 and 6
List more common multiples of 4 and 6 after 12 and 24.
Steps only
The least common multiple is 12, so keep adding 12.
Answer
36, 48, 60, 72, …
Question 1(a)
Find five common multiples of 2 and 3.
Steps only
Start with 6 and add 6 each time.
Answer
6, 12, 18, 24, 30.
Question 1(b)
Find five common multiples of 5 and 8.
Steps only
Start with 40 and add 40 each time.
Answer
40, 80, 120, 160, 200.
Question 1(c)
Find five common multiples of 2 and 4.
Steps only
Start with 4 and add 4 each time.
Answer
4, 8, 12, 16, 20.
Question 1(d)
Find five common multiples of 3 and 9.
Steps only
Start with 9 and add 9 each time.
Answer
9, 18, 27, 36, 45.
Question 1(e)
Find five common multiples of 5 and 10.
Steps only
Start with 10 and add 10 each time.
Answer
10, 20, 30, 40, 50.
Question 1(f)
Find five common multiples of 9 and 12.
Steps only
Start with 36 and add 36 each time.
Answer
36, 72, 108, 144, 180.
Question 1(g)
Find five common multiples of 8 and 12.
Steps only
Start with 24 and add 24 each time.
Answer
24, 48, 72, 96, 120.
Question 1(h)
Find five common multiples of 6 and 8.
Steps only
Start with 24 and add 24 each time.
Answer
24, 48, 72, 96, 120.
Question 1(i)
Find five common multiples of 6 and 9.
Steps only
Start with 18 and add 18 each time.
Answer
18, 36, 54, 72, 90.
Question 2
Food is at 64. Robby jumps by 4 and Deeku by 6. Who reaches it?
Steps only
64÷4=16 exactly.
64÷6 leaves a remainder of 4.
Answer
Only Robby reaches the food, after 16 jumps; Deeku never lands on 64.
Trail Jumps and Common Factors
Textbook pages 167–169
Question 3 · jumps of 2
Which named friends does the activity identify for jumps of 2?
Steps only
The marked friend positions are 4, 12, 14 and 50, and all are even.
Answer
The ant, frog, bird and rabbit at 4, 12, 14 and 50.
Question 3 · jumps of 3
Which named friends does the activity identify for jumps of 3?
Steps only
The marked positions 9, 21, 39 and 57 are divisible by 3.
Answer
The friends at 9, 21, 39 and 57.
Question 3 · jumps of 5
Which positions from 0 to 59 are touched by jumps of 5?
Steps only
Count forward in fives from 0.
Answer
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 and 55.
Question 3 · jumps of 10
Which positions from 0 to 59 are touched by jumps of 10?
Steps only
Count forward in tens from 0.
Answer
0, 10, 20, 30, 40 and 50.
Question 4(a)
Can jumps of 2 reach both 24 and 36?
Steps only
24÷2 and 36÷2 are both whole numbers.
Answer
Yes; 2 is a common factor.
Question 4(b)
Can jumps of 3 reach both 24 and 36?
Steps only
24÷3 and 36÷3 are both whole numbers.
Answer
Yes; 3 is a common factor.
Question 4(c)
Can jumps of 4 reach both 24 and 36?
Steps only
24÷4 and 36÷4 are both whole numbers.
Answer
Yes; 4 is a common factor.
Question 4(d)
What other jump lengths reach both 24 and 36?
Steps only
List the shared factors apart from 2, 3 and 4.
Answer
1, 6 and 12 steps.
Question 4(e)
List every common factor of 24 and 36.
Steps only
Factors of 24 and 36 overlap at six values.
Answer
1, 2, 3, 4, 6 and 12.
Question 4(f)
Can jumps of 1 reach both 24 and 36?
Steps only
Every whole number is divisible by 1.
Answer
Yes; 1 is a common factor of every pair of whole numbers.
Question 5
What are the common factors of 12 and 13?
Steps only
Factors of 12: 1,2,3,4,6,12.
Factors of 13: 1,13.
Answer
Only 1.
Question 6
Which of 0, 10, 16, 27, 36 and 48 can be reached by jumps of 4?
Steps only
Check divisibility by 4.
Answer
0, 16, 36 and 48.
Question 7(a)
Find the common factors of 12 and 16.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 2, 4.
Question 7(b)
Find the common factors of 8 and 12.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 2, 4.
Question 7(c)
Find the common factors of 4 and 16.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 2, 4.
Question 7(d)
Find the common factors of 2 and 9.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1.
Question 7(e)
Find the common factors of 3 and 5.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1.
Question 7(f)
Find the common factors of 12 and 15.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 3.
Question 7(g)
Find the common factors of 20 and 5.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 5.
Question 7(h)
Find the common factors of 9 and 21.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 3.
Question 7(i)
Find the common factors of 6 and 27.
Steps only
List the factors of both numbers and keep their overlap.
Answer
1, 3.
Divisibility Reasoning
Textbook pages 169–170
Question 8(a)
Factors of even numbers must be even.
Steps only
For example, 1 and 3 are odd factors of 6.
Answer
False.
Question 8(b)
Multiples of odd numbers cannot be even.
Steps only
For example, 2×3=6 is even.
Answer
False.
Question 8(c)
Factors of odd numbers cannot be even.
Steps only
An even factor multiplied by any whole number gives an even product.
Answer
True.
Question 8(d)
The product of two consecutive numbers is a common multiple of both.
Steps only
Their product is divisible by either factor.
Answer
True.
Question 8(e)
The only common factor of consecutive numbers is 1.
Steps only
Any shared factor would also divide their difference, which is 1.
Answer
True.
Question 8(f)
Zero cannot be a factor of any number.
Steps only
Division by zero is undefined, and 0×n cannot make a nonzero number.
Answer
True.
Question 9
Sher Khan hunts every 3rd day and Bagheera every 5th day. When do they hunt together?
Steps only
Common multiples of 3 and 5 are multiples of 15.
Answer
On days 15, 30, 45, 60, … after the starting day.
Question 10(a)
Mowgli must land on Baloo at 30 but avoid Sher Khan at 25. Which whole-number jump lengths work?
Steps only
Use factors of 30: 1,2,3,5,6,10,15,30.
Remove factors of 25: 1 and 5.
Answer
2, 3, 6, 10, 15 or 30 steps.
Question 10(b)
Which jump lengths let Mowgli meet both Kaa at 21 and Akela at 35?
Steps only
Common factors of 21 and 35 are 1 and 7.
Answer
1 or 7 steps.
Question 11(a)
Which listed numbers are divisible by 2 but not 5?
Steps only
Choose even numbers that do not end in 0.
Answer
22, 38, 66, 78, 62, 84 and 56.
Question 11(b)
Which listed numbers are divisible by 5 but not 2?
Steps only
Choose numbers ending in 5.
Answer
75, 45, 25, 95 and 55.
Question 11(c)
Which listed numbers are divisible by 10?
Steps only
A multiple of 10 is automatically divisible by 2 and 5.
Answer
There is no separate “10 only” group.
Question 11(d)
Which listed numbers are divisible by 2, 5 and 10?
Steps only
Choose numbers ending in 0.
Answer
90, 30 and 40.