This set of Aptitude Questions and Answers (MCQs) focuses on “HCF”.

1. Find the HCF of 2^{5}*3^{3}*5^{2}*11, 2^{4}*3^{4}*5*7, 2^{6}*3*5^{3}*13.

a) 240

b) 120

c) 480

d) 720

View Answer

Explanation: The common factor among all three numbers are 2

^{4}*3*5.

Therefore, the HCF is 2

^{4}*3*5 = 16*3*5 = 240.

2. Find the HCF of 405, 585, 765 and 900.

a) 45

b) 90

c) 35

d) 15

View Answer

Explanation: The difference between 405 and 585 is 180 = 45*4.

The difference between 585 and 765 is 180 = 45*4.

The difference between 765 and 900 is 135 = 45*3.

The difference between 405 and 900 is 495 = 45*11.

Therefore, the HCF of 405, 585, 765 and 900 is 45.

3. Two numbers are in the ratio 15:16. If the HCF is 8, find the numbers.

a) 120 and 112

b) 128 and 136

c) 120 and 128

d) 112 and 104

View Answer

Explanation: Let the two numbers be 15x and 16x, then their HCF is x.

So, x=8, hence, the numbers are 15*8 = 120 and 16*8 = 128.

4. Find the greatest number that will divide 731, 1333, 1849.

a) 41

b) 43

c) 37

d) 47

View Answer

Explanation: 731 = 43*17; 1333 = 43*31; 1849 = 43*43.

Therefore, the greatest number that will divide 731, 1333, 1849 is 43.

5. Two equilateral triangle have sides of lengths 38 and 114 respectively. A greatest length of tape that can measure both of them exactly is formed. How many such equal parts can be measured?

a) 20

b) 24

c) 27

d) 18

View Answer

Explanation: HCF of 38 and 114 is 19.

The number of such equal parts that can be measured = \(\frac{38}{19}*3+\frac{114}{19}\)*3=24.

6. The sum of two numbers is 552 and their HCF is 23. What is the minimum number of pairs that satisfy these conditions?

a) 2

b) 4

c) 1

d) 0

View Answer

Explanation: Let the two numbers be 23x and 23y.

Given, 23x + 23y = 552.

So, x + y = 24.

Now, co-prime pairs with sum 24 is (1,23), (5,19), (7,17) and (11,13).

Hence, there are 4 pairs that satisfy the conditions.

7. Two squares have sides of length 64 and 96 respectively. Find the greatest length of wire that can measure both of them exactly.

a) 32

b) 16

c) 24

d) 8

View Answer

Explanation: HCF of 64 and 96 is 32.

Therefore, the greatest length of wire that can measure both of them exactly is 32.

8. The capacity of two pots is 130 and 78 liters respectively. Find the maximum possible capacity of a container which can exactly measure the contents of 2 pots.

a) 13000 cc

b) 6500 cc

c) 26000 cc

d) 19500 cc

View Answer

Explanation: The common factors of two pots of capacity 130 and 78 liters is 6.5, 13 and 26 liters.

Therefore, the maximum possible capacity of a container which can exactly measure the contents of 2 pots is 26 liters i.e., 26000 cc.

9. A daily wage laborer was engaged for a certain number of days for Rs.5950, but being absent on some of those days he was paid only Rs.4900. What is the maximum possible daily wage?

a) 175

b) 225

c) 300

d) 350

View Answer

Explanation: HCF of 5950 and 4900 is 350.

Hence, the maximum possible daily wage is Rs.350.

10. 27 apple trees, 54 orange trees and 72 mango trees are to be planted in rows such that each row has contains the same number of trees of one variety only. Find the minimum number of rows in which the trees may be planted.

a) 9

b) 3

c) 15

d) 17

View Answer

Explanation: HCF of 27, 54 and 72 is 9.

Therefore, the minimum number of rows in which the trees may be planted is \(\frac{27}{9}+\frac{54}{9}+\frac{72}{9}\)=17.

**More Aptitude Questions and Answers on HCF:**

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