WORKSHEET REAL NUMBERS GRADE 10 NCERT / CBSE

SET - A

1.  The HCF of two numbers is 113, their LCM is 56952. If one of the numbers is 904, find the other number.

2. Using prime factorization method find the LCM of (i) 24, 36, 40   (ii) 12, 15, 20, 27 (iii) 21,28, 36, 45

3.  Find the HCF of (i) 125 and 425  (ii) 27727 and 53124 (iii) 1260 & 7344  (iv) 1648 and 4052.

4. Write the prime factorization of the following: (i) 240  (ii) 336   (iii) 844  (iv) 2400

5. Find the HCF and LCM of : (i) 570 and 1425   (ii) 56 and 77    (iii) 60 and 20    (iv) 308 and 33

6. In question  (5) verify that the product of the numbers = product of HCF & LCM

7. Explain why 7x 11 x 13 +13 and 7 x 6 x 5 x 4 x 3 x 2 x 1+5 are composite numbers.

                             SET - B 

1. Prove that the following are irrational numbers 

2. What is the smallest number that when we divided by 35, 56 and 91 leaves reminder 7 in each case.

3. Check whether 12ⁿ cannot end with the digit  0 or 5 for any natural number n.

t  is an irrational number.

                                  SET - C 

1. Using fundamental theorem of arithmetic find prime factorization of 29029 and 1740

2. Show that  is an irrational number.

3. Find the greatest number which divides 245 and 1029 leaving remainder 5 in each case.

4. Express  as a decimal fraction.

5. Prove that  is not a rational number.

6. Find the greatest number of 6 digits exactly divisible  by 24, 15 and 36

7. Express the following as a rational in the simplest form: (i) 0.36565…    (ii) 1.2244444….

8. Explain why (i) 11 x 13 x 15 x 17 + 17 is a composite number?

    (ii) 7 x 11 x 13 x 15 + 15 is a composite number?

9. Using fundamental theorem of Arithmetic, find the HCF of 6048 and 4752. Also find the LCM by the formula involving the product of two numbers and the product of HCF and LCM.

10. Check whether 9ⁿ can end with the digit 0 for any natural number n.