 # Real Numbers

Additional practice questions - Prime factorisation, LCM, HCF, Euclid's Lemma
1. #### Concept: Word Problem

Karan has 180 blue marbles and 150 red marbles. He wants to pack them into packets containing equal number of marbles of the same colour. What is the maximum number of marbles that each packet can hold?

2. #### Concept: HCF of 2 numbers - Euclid's Lemma

Find the largest number that will divide 382 and 710 and leave a remainder 13 in each case.

3. #### Concept: HCF of 3 numbers - Euclid's Lemma

What is the largest number that divides 437, 732 and 1263 leaving remainder of 24 in each case?

4. #### Concept: HCF of 2 numbers word problem

What is the largest number that divides 967 and 1767 leaving remainders of 71 and 103 respectively?

5. #### Concept: HCF of 3 numbers word problem

What is the largest number that divides 170, 220 and 420 leaving remainders 8, 4 and 15 respectively?

6. #### Concept: Prime Factorise and find LCM & HCF

i. Find LCM and HCF of 25 * 54 * 72 * 136 and 23 * 56 * 7 * 173
ii. If a, b, c, d, e, and f are prime, find LCM and HCF of a5 * b2 * c2 * d5 and a7 * b3 * e * f3

7. #### Concept: Word problem in LCM and HCF

The Muscle Gym has bought 63 treadmills and 108 elliptical machines. The gym divides them into several identical sets of treadmills and elliptical machines for its branches located throughout the city, with no exercise equipment left over. What is the greatest number of branches the gym can have in the city?

8. #### Concept: Word problem in LCM and HCF

Katya has 49 paintings and 35 medals. She wants to display them in groups throughout her house, each with the same combination of paintings and medals, with none left over. What is the greatest number of groups Katya can display?

9. #### Concept: Word problem in LCM and HCF

Anish goes fishing every 5th day and Balaji goes fishing every 7th day. If Anish and Balaji both went fishing today, how many days until they will go fishing on the same day again?

10. #### Concept: Word problem in LCM and HCF

Tamanna is arranging black marbles in groups of 13 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could have?