HCF Formulas

Question and Answer for HCF

Question : Find the Highest Common Factor of 55, 65 and 75.

A. 2
B. 3
C. 4 
D. 5

Solution:
Given, three numbers as 55, 65 and 75.

We know, 55 = 5 × 11

65 = 5 × 13

75 = 5 × 15

From the above expression, we can say 5 is the only common factor for all three numbers.

Therefore, 5 is the HCF of 55, 65 and 75.

Question : 6 and 7 are two co-prime numbers. Using these numbers verify the HCF formula, LCM of Co-prime Numbers = Product of the numbers.

A. 45

B. 46

C. 42

D. 47

Solution: Let’s find the LCM and HCF of 6 and 7

6 = 1×2×3

7= 1×7

LCM = 1×2×3×7 = 42 HCF = 1

The HCF formula states that LCM of Co-prime Numbers = Product of the numbers

Product of the numbers = 6×7 = 42

Hence, LCM of Co-prime Numbers = Product of the numbers i.e. 42 = 42. Therefore, it is verified.

Question  : Find the HCF of 18/10, 12/15, 24/20, 30/5

A. 3/400

B. 4/500

C. 6/400

D. 8/400

Solution: According to the HCF formula, HCF = HCF of numerator/LCM of the denominator.

So finding the HCF of the numerators:

18 = 2×3×3

12 = 2×2×3

24 = 2×2×2×3

30 = 2×5 × 3

Therefore, the HCF of 9, 8, 12, 18 = 3

10 = 1×2×5

15 = 1×3×5

20 = 1×2×4×5

5 = 1×5

Therefore, the LCM of 10, 15, 20, 5 = 2×5×2×4×5 = 400

HCF = HCF of numerators/LCM of the denominators

HCF = 3/400

Therefore, the HCF of 9/10, 6/15, 12/20, 18/5 is 3/400.

Question : Rakesh joshi has calculated the H.C.F. and L.C.M. of two 2- digit numbers as16 and 480 respectively. The numbers are :

A. 40, 48
B. 60, 72
C. 64, 80
D. 80, 96

Ans: 80, 96
H.C.F. of the two 2-digit numbers= 16
Hence, the numbers can be expressed as 16x and 16y, where x and y are prime to each other.
Now,
First number \times second number = H.C.F. \times L.C.M.
=> 16x \times 16y = 16 \times 480
=> xy = 16 \times \frac{480}{16} \times 16= 30 ´
The possible pairs of x and y, satisfying the condition xy = 30 are :
(3, 10), (5, 6), (1, 30), (2, 15)
So the numbers are (48,160) (80,96)

Question : The HCF of the two numbers is 29 & their sum is 174. What are the numbers?

A. 29 and 145
B. 30 and 150
C. 40 and 140
D. 65 and 130

Solution:

Let the two numbers be 29x and 29y.

Given, 29x + 29y = 174

29(x + y) = 174

x + y = 174/29 = 6

Since x and y are co-primes, therefore, possible combinations would be (1,5), (2,4), (3,3).

The only combination that follows the co-prime part is (1,5)

For (1,5): 29 x = 29 x 1 and 29 y = 29 (5) = 145

Therefore, the required numbers are 29 and 145.