Given below are the Class 10 Maths Real Numbers Worksheets

a. HCF and LCM problems

b. Prime Factorisation Problems

c. Division Problems

d. Long answer questions

e. Word Problems

Question 1

Use Euclid’s algorithm to find the HCF of 4052 and 12576.

Question 2

show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

Question 3

Find HCF and LCM of following using Fundamental Theorem of Arithmetic method.

448, 1008 and 168

Find HCF and LCM of following using Fundamental Theorem of Arithmetic method.

448, 1008 and 168

Question 4

Find the HCF and LCM of following using Fundamental Theorem of Arithmetic method 377, 435 and 667.

Find the HCF and LCM of following using Fundamental Theorem of Arithmetic method 377, 435 and 667.

Question 5

Find HCF of numbers 134791, 6341 and 6339 by Euclid’s division algorithm.

Find HCF of numbers 134791, 6341 and 6339 by Euclid’s division algorithm.

Question 6

Find the least positive integer which when diminished by 5 is exactly divisible by 36 and 54.

Find the least positive integer which when diminished by 5 is exactly divisible by 36 and 54.

Question 7

Find HCF and LCM of 12, 63 and 99 using prime factorisation method.

Find HCF and LCM of 12, 63 and 99 using prime factorisation method.

Question 8

If the HCF of 144 and 180 is expressed in the form 13m – 3, find the value of m.

If the HCF of 144 and 180 is expressed in the form 13m – 3, find the value of m.

Question 9

Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together?

Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together?

Question 10

In sports Day activities of a school, three cyclists start together and can cycle 48 km, 60 km and 72 km a day round the field. The field is circular, whose circumference is 360 km. After how many rounds they will meet again?

In sports Day activities of a school, three cyclists start together and can cycle 48 km, 60 km and 72 km a day round the field. The field is circular, whose circumference is 360 km. After how many rounds they will meet again?

Question 11

LCM of two numbers is 2295 and HCF is 9. If one of the numbers is 153, find the other number.

LCM of two numbers is 2295 and HCF is 9. If one of the numbers is 153, find the other number.

Question 12

Express 111972 as a product of its prime factors.

Question 13

Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of tanker which can measure the petrol of either tanker in exact number of times.

Question 14

The traffic lights at three different road – crossing change after every 36 seconds, 60 seconds and 72 seconds. If they change simultaneously at 8 a. m. after, what time will they change again simultaneously?

The traffic lights at three different road – crossing change after every 36 seconds, 60 seconds and 72 seconds. If they change simultaneously at 8 a. m. after, what time will they change again simultaneously?

Question 15

Using prime factorization method, find HCF and LCM of 80, 124 and 144. Also, show that HCFX LCM = Product of three numbers.

Using prime factorization method, find HCF and LCM of 80, 124 and 144. Also, show that HCFX LCM = Product of three numbers.

Question 17

Determine the prime factorization of 45470971 positive integers.

Determine the prime factorization of 45470971 positive integers.

Question 18

A rectangular courtyard is 18m 72 cm long and 13m 20cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

A rectangular courtyard is 18m 72 cm long and 13m 20cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Question 19

Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

Question 20

What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?

What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?