CBSE Class 6 Mathematics Prime Time Worksheet Set 01

Very Short Answer Questions

Question 1. What is meant by a factor of a number? Give one example.
Answer:
A factor of a number is a number that divides it exactly, leaving remainder 0.
Example: 4 is a factor of 12, because 12 ÷ 4 = 3 with nothing left over.

Teacher's Note:
1. ‘Divides exactly’ means remainder 0.
2. Every number has 1 and itself as factors.

Question 2. Write the first five multiples of 7.
Answer:
7 × 1, 7 × 2, 7 × 3, 7 × 4, 7 × 5 give 7, 14, 21, 28 and 35.

Teacher's Note:
1. Multiples come from the multiplication table.
2. A number has endless multiples.

Question 3. In the idli-vada game played with multiples of 3 and multiples of 5, write the first two numbers for which the children have to say ‘idli-vada’.
Answer:
‘Idli-vada’ comes at the common multiples of 3 and 5.
The first two are 15 and 30.

Teacher's Note:
1. 3 and 5 are co-prime, so the first common multiple is 3 × 5.
2. The next one is double that.

Question 4. Write all the common factors of 10 and 15.
Answer:
Factors of 10: 1, 2, 5, 10. Factors of 15: 1, 3, 5, 15.
Common factors: 1 and 5.

Teacher's Note:
1. Write both lists, then pick the shared numbers.
2. 1 is always common.

Question 5. Define a prime number and give one example.
Answer:
A prime number has exactly two factors, 1 and the number itself.
Example: 13, whose only factors are 1 and 13.

Teacher's Note:
1. The word ‘exactly’ is important.
2. Any prime is a correct example.

Question 6. Why is 1 neither a prime number nor a composite number?
Answer:
1 has only one factor, which is 1 itself.
A prime needs exactly two factors and a composite needs more than two, so 1 is neither.

Teacher's Note:
1. Compare the number of factors with each definition.
2. This is a favourite one-mark question.

Question 7. Write all the prime numbers that lie between 20 and 30.
Answer:
21 = 3 × 7, 22, 24, 26, 28 are even, 25 = 5 × 5 and 27 = 3 × 9.
The primes left are 23 and 29.

Teacher's Note:
1. Strike out the even numbers first.
2. Then test 3 and 5 on the rest.

Question 8. How many prime numbers are there between 1 and 100?
Answer:
There are 25 prime numbers between 1 and 100.

Teacher's Note:
1. The Sieve of Eratosthenes gives this list.
2. The largest of them is 97.

Question 9. Name the method that is used to list all the prime numbers from 1 to 100 by crossing out multiples.
Answer:
It is the Sieve of Eratosthenes: cross out 1, then the other multiples of 2, 3, 5, 7, …; the circled numbers left are the primes.

Teacher's Note:
1. A sieve lets the primes through and catches the rest.
2. Spell the name correctly.

Question 10. What are co-prime numbers? Give one example.
Answer:
Two numbers are co-prime if their only common factor is 1.
Example: 4 and 9 (factors 1, 2, 4 and 1, 3, 9).

Teacher's Note:
1. Co-prime describes a pair, not one number.
2. Neither number need be prime.

Question 11. Write the prime factorisation of 36.
Answer:
36 = 4 × 9 = (2 × 2) × (3 × 3), so 36 = 2 × 2 × 3 × 3.

Teacher's Note:
1. Keep breaking until every factor is prime.
2. Write the primes in increasing order.

Question 12. State the test for divisibility by 5.
Answer:
A number is divisible by 5 when its last digit is 0 or 5.
Example: 2345 ends in 5, so it is divisible by 5.

Teacher's Note:
1. Only the last digit matters for 5.
2. Give an example to support the rule.

Question 13. In the jump game, treasures are kept on 16 and on 24. Write all the jump sizes, other than 1, with which Jumpy can land on both the treasures.
Answer:
The jump size must be a common factor of 16 and 24: 1, 2, 4 and 8.
Leaving out 1, the jump sizes are 2, 4 and 8.

Teacher's Note:
1. Landing on a number means the jump size divides it.
2. Read the question: 1 is excluded.

Question 14. Write all the common factors of 18 and 24.
Answer:
Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors: 1, 2, 3 and 6.

Teacher's Note:
1. Factor pairs make the lists quickly.
2. Circle the numbers present in both lists.

Question 15. Find the smallest number that is a common multiple of 4 and 10.
Answer:
Multiples of 4: 4, 8, 12, 16, 20, … Multiples of 10: 10, 20, …
The smallest common multiple is 20.

Teacher's Note:
1. List the multiples of the bigger number and test each.
2. Here 4 × 10 = 40 is not the smallest.

Question 16. Is 91 a prime number? Give a reason for your answer.
Answer:
No. 91 = 7 × 13, so it has four factors: 1, 7, 13 and 91.
So 91 is a composite number.

Teacher's Note:
1. 91 is a well-known trap; test 7.
2. One extra factor is enough to show a number is composite.

Question 17. Write the pair of twin primes that lies between 35 and 50.
Answer:
The primes between 35 and 50 are 37, 41, 43, 47.
Only 41 and 43 differ by 2, so the pair is 41 and 43.

Teacher's Note:
1. List the primes first, then check the gaps.
2. Twin primes differ by exactly 2.

Question 18. Write three consecutive composite numbers that lie between 20 and 30.
Answer:
24, 25 and 26: 24 = 2 × 12, 25 = 5 × 5 and 26 = 2 × 13. (24, 25, 26, 27, 28 are all composite, so other answers such as 25, 26, 27 are also correct.)

Teacher's Note:
1. Look for a stretch between two primes.
2. Show one factor of each to justify.

Question 19. Are 21 and 22 co-prime? Give a reason for your answer.
Answer:
Yes. 21 = 3 × 7 and 22 = 2 × 11 have no prime factor in common, so their only common factor is 1.

Teacher's Note:
1. Two consecutive numbers are always co-prime.
2. Prime factorisation makes the check quick.

Question 20. The prime factorisation of a number has one 2, two 3s and one 5. Which number is it?
Answer:
The number is 2 × 3 × 3 × 5 = 90.

Teacher's Note:
1. Multiply all the primes, repeating each as often as stated.
2. Check: 90 = 9 × 10.

Question 21. Using the divisibility test for 4, check whether 3718 is divisible by 4.
Answer:
The last two digits of 3718 form 18, and 18 is not a multiple of 4.
So 3718 is not divisible by 4.

Teacher's Note:
1. Being even is not enough for 4.
2. Look only at the last two digits.

Question 22. Which of the numbers 2, 4, 5, 8 and 10 are factors of 4500?
Answer:
4500 ends in 0, so 2, 5 and 10 are factors. Its last two digits are 00, so 4 is a factor.
Its last three digits form 500, which is not a multiple of 8, so 8 is not a factor.
Factors: 2, 4, 5 and 10.

Teacher's Note:
1. Use a separate test for each number.
2. 500 ÷ 8 = 62 remainder 4.

Question 23. Using prime factorisation, show whether 84 is divisible by 14.
Answer:
84 = 2 × 2 × 3 × 7 and 14 = 2 × 7.
The primes of 14 (one 2 and one 7) are present in 84, so 84 is divisible by 14: 84 = 14 × 6.

Teacher's Note:
1. The divisor’s primes must all be inside the number’s factorisation.
2. The left-over primes give the quotient: 2 × 3 = 6.

Question 24. In the box of numbers 7, 12, 25 and 31, which number is special because it is the only even number in the box?
Answer:
7, 25 and 31 are odd, so 12 is the only even number.

Teacher's Note:
1. Even numbers end in 0, 2, 4, 6 or 8.
2. Check each number in the box.

Question 25. Write one pair of composite numbers, both smaller than 12, that are co-prime to each other, and give the reason.
Answer:
8 and 9. 8 = 2 × 2 × 2 and 9 = 3 × 3 are both composite but share no prime factor, so their only common factor is 1.
(4 and 9 is another correct pair.)

Teacher's Note:
1. Pick one number made of 2s and one made of 3s.
2. Give the factorisations as the reason.

Question 26. For a certain pair of numbers, the first common multiple is equal to the product of the two numbers. What does this tell you about the pair? Give one example.
Answer:
It tells us the two numbers are co-prime.
Example: 4 and 9; their first common multiple is 36 = 4 × 9.

Teacher's Note:
1. Co-prime pairs share nothing, so the product is the first meeting point.
2. Compare with 6 and 10, whose first common multiple 30 is less than 60.

Question 27. A number is divisible by 8 and also by 10. Which of the numbers 2, 4 and 5 must certainly divide it?
Answer:
All three. Being divisible by 8 makes it divisible by 2 and 4, and being divisible by 10 makes it divisible by 2 and 5.

Teacher's Note:
1. A factor of a factor is also a factor.
2. 8 = 2 × 4 and 10 = 2 × 5.

Question 28. Using prime factorisation, explain why 42 is not divisible by 12.
Answer:
42 = 2 × 3 × 7 and 12 = 2 × 2 × 3.
12 needs two 2s, but 42 has only one 2. So the factorisation of 12 is not inside that of 42, and 42 is not divisible by 12.

Teacher's Note:
1. Count how many times each prime appears.
2. One missing prime is enough to say ‘not divisible’.

Question 29. What is the smallest number whose prime factorisation has three different prime numbers?
Answer:
Use the three smallest primes: 2 × 3 × 5 = 30.

Teacher's Note:
1. Smallest primes give the smallest product.
2. The next such number is 2 × 3 × 7 = 42.

Question 30. Find the largest three-digit number that is divisible by 8.
Answer:
1000 = 8 × 125 is the first four-digit multiple of 8.
So the one before it, 1000 − 8 = 992 = 8 × 124, is the largest three-digit multiple of 8.

Teacher's Note:
1. Start from the smallest four-digit number and step back.
2. Check with the test: 992 is itself the last three digits.