Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the prime factorization of 56. 56 = × × ×

(2) Find the HCF of 36 and 48 using the prime factorization method. HCF =

Perfect! HCF takes the lowest powers of common prime factors.

(3) State the Fundamental Theorem of Arithmetic. Every number can be expressed as a of , and this is unique, apart from the of the prime .

(4) Write the first 3 multiples of 9. , ,

(5) Find the LCM of 4 and 5.

Correct! Since 4 and 5 are coprime, LCM = 4 × 5 = 20.

Short Answer Questions (2 Marks Each)

Answer each question with proper working

(1) Find the HCF of 24 and 36 by Euclid's division lemma. HCF =

Perfect! When remainder becomes 0, the divisor is the HCF.

(2) Express 98 as the product of prime factors.

98 = 2×722×32×7

(3) Find the LCM and HCF of 20 and 28 and verify that HCF × LCM = Product of the numbers. HCF = and LCM =

(4) Find the HCF of 90 and 144 using the prime factorization method. HCF =

Excellent! HCF = 18.

(5) Find the LCM of 15 and 25 using the division method. LCM =

Perfect! LCM = 75.

Long Answer Questions (4 Marks Each)

(1) Using Euclid's division lemma, show that the square of any positive integer is of the form 3m or 3m+1.

(2) Find the HCF of 306 and 657 using Euclid's algorithm. HCF =

Perfect! HCF of 306 and 657 = 9.

(3) Find the LCM and HCF of 72 and 120 and verify the relation between them. HCF = and LCM =

(4) A merchant has 120 litres of oil of one kind and 180 litres of another. He wants to sell the oil by filling equal quantities into containers without mixing the two kinds. What is the greatest capacity of such a container?

Excellent! Greatest capacity = 60 litres.

(5) Show that 5 is an irrational number.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The HCF of 42 and 70 is:

(a) 7 (b) 14 (c) 21 (d) 28

Correct! 42 = 2 × 3 × 7, 70 = 2 × 5 × 7, so HCF = 2 × 7 = 14.

(2) Prime factorization of 84 is:

(a) 22 × 3 × 7 (b) 2 × 3 × 14 (c) 22 × 3 × 7 (d) 22 × 7 × 3

Correct! 84 = 4 × 21 = 22 × 3 × 7.

(3) The LCM of 6 and 8 is:

(a) 12 (b) 18 (c) 24 (d) 48

Correct! 6 = 2 × 3, 8 = 23, so LCM = 23 × 3 = 24.

(4) Which of the following is NOT a prime number?

(a) 13 (b) 17 (c) 19 (d) 21

Correct! 21 = 3 × 7, so it's composite, not prime.

(5) According to Euclid's division lemma, for given integers a and b (with a > b), there exist integers q and r such that:

(a) a = bq + r, 0 ≤ r < b (b) a = qb + r, 0 < r ≤ b (c) a = qb + r, 0 ≤ r ≤ b (d) None of these

Correct! Euclid's division lemma: a = bq + r, where 0 ≤ r < b.

(6) HCF of 8 and 12 is:

(a) 2 (b) 3 (c) 4 (d) 6

Correct! 8 = 23, 12 = 22 × 3, so HCF = 22 = 4.

(7) The LCM of 14 and 21 is:

(a) 28 (b) 42 (c) 56 (d) 84

Correct! 14 = 2 × 7, 21 = 3 × 7, so LCM = 2 × 3 × 7 = 42.

(8) The smallest prime number is:

(a) 0 (b) 1 (c) 2 (d) 3

Correct! 2 is the smallest and only even prime number.

(9) The product of HCF and LCM of 8 and 12 is:

(a) 48 (b) 96 (c) 24 (d) 36

Correct! HCF = 4, LCM = 24, so HCF × LCM = 4 × 24 = 96 = 8 × 12.

(10) Which of these is irrational?

(a) 4 (b) 9 (c) 5 (d) 3

Correct! 5 is irrational because 5 is not a perfect square.

Number Theory Concepts True or False

Determine whether these statements are True or False:

Real Numbers Quiz