Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Is 31 a prime or composite number?
Perfect! 31 is prime because it has exactly two factors: 1 and 31.
(2) Write any two co-prime numbers.
Excellent! Co-prime numbers have HCF = 1.
(4) Is 33 divisible by 3? Give reason.
Right! Sum of digits: 3+3 = 6, which is divisible by 3.
(6) What is the greatest factor of a number?
Perfect! Every number is its own greatest factor.
(10) Give one example of a pair of numbers with LCM 12.
Great! Any pair whose LCM is 12 works.
Short Answer Questions (2 Marks Each)
Answer each question in 2-3 sentences
(1) Find the HCF of 18 and 24 by the common factor method. HCF =
Excellent! The highest common factor is 6.
(2) Find the LCM of 5 and 15 using the division method. LCM is:
Perfect! When one number is a multiple of another, LCM = larger number.
(3) Check whether 132 is divisible by 2, 3, and 11.
Divisible by 2:
Divisible by 3:
Divisible by 11:
Excellent! 132 ends in 2 (even), sum of digits = 6 (divisible by 3), and 132÷11 = 12.
(4) Write the prime factorisation of 36. 36 =
Perfect! 36 =
(5) Write two numbers whose HCF is 1 but LCM is 30.
First number:
Second number:
Great! HCF(5,6) = 1 and LCM(5,6) = 30. They are co-prime.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Find the HCF and LCM of 20 and 28 by prime factorisation. Verify using the relation: HCF × LCM = Product of the two numbers. HCF =
Perfect! The relation is verified: HCF × LCM = 20 × 28.
(2) Three traffic lights blink at intervals of 12, 15, and 20 seconds. If they blink together at 9:00 a.m., at what time will they blink together again? LCM =
Time =
Excellent! They will blink together again at 9:01 a.m.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) Which of the following is a prime number?
(a) 21 (b) 9 (c) 29 (d) 33
Correct! 29 is prime (only factors are 1 and 29). Others are composite.
(2) LCM of 3 and 7 is:
(a) 10 (b) 14 (c) 21 (d) 24
Correct! Since 3 and 7 are co-prime, LCM = 3 × 7 = 21.
(3) HCF of 36 and 48 is:
(a) 6 (b) 12 (c) 18 (d) 24
Correct! HCF(36,48) = 12. Both are divisible by 12.
(4) Which number is divisible by 9?
(a) 243 (b) 244 (c) 124 (d) 123
Correct! Sum of digits in 243: 2+4+3 = 9, which is divisible by 9.
(5) Prime factors of 100 are:
(a) 2 and 5 (b) 10 and 10 (c) 4 and 25 (d) 20 and 5
Correct! 100 = 2² × 5², so prime factors are 2 and 5.
(6) Which pair of numbers are not co-prime?
(a) 7 and 10 (b) 4 and 9 (c) 3 and 8 (d) 6 and 12
Correct! HCF(6,12) = 6 ≠ 1, so they are not co-prime.
(7) 2 is a factor of:
(a) 5 (b) 9 (c) 10 (d) 15
Correct! 10 ÷ 2 = 5, so 2 is a factor of 10.
(8) What is the product of LCM and HCF of 8 and 12?
(a) 96 (b) 48 (c) 24 (d) 36
Correct! HCF(8,12) = 4, LCM(8,12) = 24, Product = 4 × 24 = 96.
(9) Total number of factors of 18 are:
(a) 2 (b) 4 (c) 6 (d) 5
Correct! Factors of 18: 1, 2, 3, 6, 9, 18. Total = 6 factors.
(10) What is the least prime number greater than 50?
(a) 51 (b) 53 (c) 55 (d) 57
Correct! 53 is prime. 51=3×17, 55=5×11, 57=3×19 are composite.
Number Properties Challenge
Determine whether these statements about numbers are True or False: