CLASS 5TH MATHS WORKSHEET LESSON 13.

Mathematics Worksheet: Factors & Multiples, Animal Jumps (Preparatory Stage)

Based on NCERT "Animal Jumps" chapter. Each section below has 10 questions—attempt, check answer, then see the detailed solution!

Concepts

• What is a factor of a number?
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  Answer: A number that divides another number completely (no remainder).

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  Solution: For example, 2 is a factor of 12 because 12 ÷ 2 = 6 (no remainder).
• Define a multiple.
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  Answer: The result when a number is multiplied by any other number.

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  Solution: Example: 12 is a multiple of 3 because 3 × 4 = 12.
• What is a common multiple?
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  Answer: A number that is a multiple of two or more numbers.

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  Solution: Example: 12 is a common multiple of 3 and 4.
• Which is the smallest common multiple of 3 and 4?
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  Answer: 12

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  Solution: Both 3 and 4 divide 12 without remainder.
• What is a prime number?
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  Answer: A number with exactly two factors: 1 and itself.

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  Solution: Example: 5 is only divisible by 1 and 5.
• Is 1 a factor of every number?
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  Answer: Yes

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  Solution: 1 × any number = the number itself.
• If a number is a multiple of 2 and 3, is it also a multiple of 6?
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  Answer: Yes, if it is a common multiple of 2 and 3.

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  Solution: All common multiples of 2 and 3 are multiples of 6.
• What do you call a number that has only two factors: 1 and itself?
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  Answer: Prime number

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  Solution: E.g., 2, 3, 5, 7, 11, etc.
• Is every multiple of 5 also a multiple of 10?
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  Answer: No

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  Solution: Example: 15 is a multiple of 5, but not of 10.
• What is the only common factor of 13 and 12?
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  Answer: 1

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  Solution: 13 is prime, no other factors except 1 with 12.

Computational Skills

• List all factors of 15.
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  Answer: 1, 3, 5, 15

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  Solution: 15 ÷ 1 = 15, ÷ 3 = 5, ÷ 5 = 3, ÷ 15 = 1.
• Find all multiples of 4 up to 20.
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  Answer: 4, 8, 12, 16, 20

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  Solution: 4 × 1, 2, 3, 4, 5.
• Write the first 5 common multiples of 2 and 3.
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  Answer: 6, 12, 18, 24, 30

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  Solution: Count up in 6s: 6 × 1, 2, 3, 4, 5.
• If a frog jumps 3 each time, which numbers will it touch up to 30?
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  Answer: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

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  Solution: Multiples of 3 up to 30.
• If a rabbit jumps 4 each time, which numbers will it touch up to 32?
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  Answer: 0, 4, 8, 12, 16, 20, 24, 28, 32

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  Solution: Multiples of 4.
• List all factors of 12.
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  Answer: 1, 2, 3, 4, 6, 12

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  Solution: Check division: 12 ÷ 1, 2, 3, 4, 6, 12.
• Write all numbers from 1 to 20 divisible by both 2 and 5.
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  Answer: 10, 20

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  Solution: 2 × 5 = 10; check multiples.
• Are 9 and 21 co-prime numbers?
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  Answer: No

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  Solution: Both divisible by 3 (GCD is 3).
• Find the common factors of 20 and 5.
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  Answer: 1, 5

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  Solution: 5 is a factor of both.
• State True or False: The only common factor of any two consecutive numbers is 1.
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  Answer: True

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  Solution: They are always co-prime.

Problem-Solving & Real-World Modeling

• If a frog takes jumps of 5 and a rabbit takes jumps of 10, what common numbers will they land on within 50?
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  Answer: 0, 10, 20, 30, 40, 50

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  Solution: Multiples of 10; both get there by their own jump pattern.
• Which of these numbers are multiples of 6 and 8: 12, 18, 24, 30, 36, 40, 48, 54, 60?
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  Answer: 24, 48, 60

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  Solution: Least common multiples: 6 × 4 = 24, 8 × 3 = 24, etc.
• Sher Khan hunts every 3rd day, Bagheera every 5th. Which days do they both hunt together within 30 days?
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  Answer: Days 15 and 30

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  Solution: Multiples of 15 are common.
• Find all factors of 32 using arrays.
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  Answer: 1, 2, 4, 8, 16, 32

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  Solution: Possible rectangles/arrays: 1×32, 2×16, 4×8, etc.
• Mowgli wants to meet both Kaa (at 21) and Akela (at 35) by jumping consistent steps from 0. What jump length could get him to both?
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  Answer: 7

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  Solution: 21 ÷ 7 = 3; 35 ÷ 7 = 5
• Which numbers between 1 and 100 are divisible by 2, 5, AND 10?
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  Answer: 10, 20, 30, ..., 100 (every 10)

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  Solution: Multiples of 10.
• A spider jumps by 3, and a grasshopper jumps by 6. What common numbers will both touch under 30?
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  Answer: 0, 6, 12, 18, 24, 30

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  Solution: Multiples of 6
• List True/False: (a) Factors of an even number must be even. (b) Zero is a factor of every number. (c) A factor of a number is always less than or equal to the number.
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  Answer: (a) False (b) False (c) True

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  Solution: Review factor definition: zero never a factor, odd factors possible, factor is by definition ≤ the number.
• Sort: 90, 22, 38, 30, 75, 45, 66, 78, 62, 40, 84, 56, 25, 95, 55. Which are divisible by 2 only? 5 only? 10 only? 2, 5 & 10?
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  Answer: Div by 2 only: 22, 38, 66, 78, 62, 84, 56; 5 only: 25, 95, 55, 75, 45; 10 only: none; 2, 5, 10: 90, 30, 40

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  Solution: Test divisibility by each.
• Challenge: Robby the rabbit and Deeku the deer both start at 0; Robby jumps 4 and Deeku 6 per hop. Where will both meet within first 50? Who reaches food first if it's at 24?
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  Answer: Common in 0, 12, 24, 36, 48. Both can reach 24 (first common), Robby needs 6 jumps, Deeku needs 4.

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  Solution: Multiples of LCM(4,6) = 12; first common after 0 is 12, then 24, etc.; 24 ÷ 4 = 6 steps, 24 ÷ 6 = 4 steps.