Class 5 Mathematics · Chapter 13

13. Animal Jumps

Solutions to all Let Us Do questions and in-chapter activities. CBSE / NCERT Class 5 Maths Mela.

Find the Hidden Numbers

1Numbers put in the box get multiplied by a number. 28, 36, 48 and 72 come out.

(a) The multiplier can be 4. All four numbers are in the table of 4.

(b) Yes. The multiplier can also be 2 or 1. 1, 2 and 4 are common factors of 28, 36, 48 and 72.

2Are there other numbers that are factors of 15? Try to make other arrays for 15.

15 can be arranged as 1 × 15 and 3 × 5.

Factors of 15 are 1, 3, 5 and 15.

3Do you see why 12 is a multiple of 1, 2, 3, 4, 6 and 12? Fill in the blanks.

2 × 6 = 12
3 × 4 = 12
12 × 1 = 12
1 × 12 = 12

Each of these numbers divides 12 completely. So, 12 is a multiple of each of them.

Let Us Do

1Make different arrays for the following numbers. Identify the factors in each case.

Number	Arrays	Factors
(a) 10	1 × 10, 2 × 5	1, 2, 5, 10
(b) 14	1 × 14, 2 × 7	1, 2, 7, 14
(c) 13	1 × 13	1, 13
(d) 20	1 × 20, 2 × 10, 4 × 5	1, 2, 4, 5, 10, 20
(e) 25	1 × 25, 5 × 5	1, 5, 25
(f) 32	1 × 32, 2 × 16, 4 × 8	1, 2, 4, 8, 16, 32
(g) 37	1 × 37	1, 37
(h) 46	1 × 46, 2 × 23	1, 2, 23, 46
(i) 54	1 × 54, 2 × 27, 3 × 18, 6 × 9	1, 2, 3, 6, 9, 18, 27, 54

Why are 13 and 37 prime numbers? They have only two factors — 1 and the number itself. They can be arranged only in a single line.

Animal Jumps

1A rabbit jumps 4 each time and a frog jumps 3 each time. What are some other common multiples of 3 and 4? What do you notice?

Common multiples of 3 and 4: 12, 24, 36, 48, 60, …

They are all multiples of 12. The gap between them is always 12.

2A spider jumps 3 and a grasshopper jumps 6. Find the common multiples of 3 and 6. What do you notice?

Common multiples of 3 and 6: 6, 12, 18, 24, 30, …

Every multiple of 6 is also a multiple of 3. So, the common multiples are just the multiples of 6.

312 and 24 are two common multiples of 4 and 6. List a few more.

36, 48, 60, 72, …

Let Us Do

1Find 5 common multiples of the following pairs of numbers.

(a) 2 and 3: 6, 12, 18, 24, 30

(b) 5 and 8: 40, 80, 120, 160, 200

(d) 3 and 9: 9, 18, 27, 36, 45

(e) 5 and 10: 10, 20, 30, 40, 50

(f) 9 and 12: 36, 72, 108, 144, 180

(f) 8 and 12: 24, 48, 72, 96, 120

(g) 6 and 8: 24, 48, 72, 96, 120

(h) 6 and 9: 18, 36, 54, 72, 90

What we notice: The common multiples come at equal gaps. If one number is a multiple of the other (like 3 and 9), the common multiples are the multiples of the bigger number. If two numbers have no common factor other than 1 (like 2 and 3, or 5 and 8), the first common multiple is their product.

2Robby the rabbit jumps 4 each time. Deeku the deer jumps 6 each time. Food is at 64. Will both reach the food? Who will reach first?

Robby lands on 4, 8, 12, …, 60, 64. 64 is a multiple of 4. So, Robby reaches the food in 16 jumps.

Deeku lands on 6, 12, 18, …, 60, 66. 64 is not a multiple of 6. So, Deeku cannot land on the food. He jumps from 60 to 66 and goes past it.

So, only Robby reaches the food.

3Which of Mowgli’s friends will he be able to visit if he jumps by 2 steps starting from 0?

He touches only even numbers. He will meet the ant (4), frog (12), bird (14) and rabbit (50).

If he jumps by 3 steps, he will meet the friends at 9, 21, 39 and 57 (spider, snake, deer and monkey).

By 5 steps, he touches 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. 5 is a common factor of these numbers.

By 10 steps, he touches 10, 20, 30, 40, 50. 10 is a common factor of these numbers.

4Let us find some common factors of 24 and 36.

(a) Yes. 2 is a common factor of 24 and 36.

(b) Yes. 3 is a common factor of 24 and 36.

(d) Jumps of 6 and 12 also reach both 24 and 36.

(e) There are 6 common factors: 1, 2, 3, 4, 6 and 12.

(f) Yes. Jumps of 1 step reach every number. 1 is a common factor of all numbers.

5What are the common factors of 12 and 13?

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 13: 1, 13.

The only common factor is 1.

6Which of the numbers 10, 16, 27, 36 and 48 can be reached by jumps of 4 steps?

16, 36 and 48 can be reached. 10 and 27 cannot.

4 is the common factor of the numbers 16, 36 and 48.

7Find the common factors of the following pairs of numbers.

(a) 12 and 16: 1, 2, 4
(b) 8 and 12: 1, 2, 4
(c) 4 and 16: 1, 2, 4

(d) 2 and 9: 1
(e) 3 and 5: 1
(f) 12 and 15: 1, 3

(f) 20 and 5: 1, 5
(g) 9 and 21: 1, 3
(h) 6 and 27: 1, 3

What we notice: 1 is a common factor of every pair. When one number is a factor of the other (like 4 and 16), all factors of the smaller number are common factors.

8State whether the following statements are true (T) or false (F).

(a) Factors of even numbers must be even. — F (3 is a factor of 6.)

(b) Multiples of odd numbers cannot be even. — F (6 is a multiple of 3.)

(d) One of the common multiples of two consecutive numbers is their product. — T (4 × 5 = 20)

(e) The only common factor of any two consecutive numbers is 1. — T

(f) 0 cannot be a factor of any number. — T

9Sher Khan hunts every 3rd day. Bagheera hunts every 5th day. If both start on the same day, on which days will they hunt together?

Common multiples of 3 and 5: 15, 30, 45, …

They will hunt together on the 15th, 30th, 45th day and so on (every 15th day).

10Answer the questions about Mowgli’s jumps.

(a) Baloo is at 30 and Sher Khan at 25. The jump must divide 30 but not 25.

Mowgli can jump 2, 3, 6, 10, 15 or 30 steps at a time. (Not 1 or 5, because they touch 25.)

(b) Common factors of 21 and 35 are 1 and 7. He can jump 7 steps (or 1 step) at a time.

11Sort the numbers into those divisible by 2 only, 5 only, 10 only, and 2, 5 and 10.

Divisible by 2 only: 22, 38, 56, 62, 66, 78, 84

Divisible by 5 only: 25, 45, 55, 75, 95

Divisible by 10 only: None. Every number divisible by 10 is also divisible by 2 and 5.

Divisible by 2, 5 and 10: 30, 40, 90

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