# Tips and Tricks and Shortcuts of HCF Questions

## Tips and Tricks of HCF Questions

What is HCF ? Suppose there are two integers a and b. There is another Suppose there are two integers a and b. There is another integer c which divides each of the integers i.e. a and b. Then, integer c is the Highest Common Factor. This page is all about Tips and Tricks of HCF Questions

### HCF – Tips and Tricks and Shortcuts

• Here, are some easy tips and tricks for you on HCF problems Learn tricks on HCF that are asked in most in most competitive exams and other recruitment exams.
• The H.C.F of two or more numbers is smaller than or equal to the smallest number of given numbers
• The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)
• The greatest number which divide x, y, z to leave remainders a, b, c is H.C.F of (x – a), (y – b) and (z – c)
•  HCF of a given number always divides its LCM.

### Type 1: Find the least or greatest number

Question 1 .The H.C.F. of two numbers is 40 and the other two factors of their L.C.M. are 15 and 20. Find the larger number?

Options

A. 600

B. 460

C. 800

D. 1400

Solution:     The numbers are 40 * 15 and 40 * 20

40 * 15 = 600

40 * 20 = 800

Correct option: C

### Type 2: Shortcuts To Find HCF

Question 2. Find the HCF of $\frac{3}{10}, \frac{4}{7}, \frac{6}{5}, and \frac{2}{9}$

Options

A. $\frac{1}{630}$

B. $\frac{3}{630}$

C. $\frac{2}{543}$

D. 630

Solution     We know that

HCF = HCF of Numerator/LCM of Denominators

HCF = $\frac{HCF(3,4,6,2)}{LCM(10,7,6,9)}$

HCF = $\frac{1}{630}$

Correct Option : A

### Tips and Tricks and Shortcuts to find HCF easily

Question. 3  Find HCF of 12 and 16.

Options

(A) 5

(B) 4

(C) 12

(D) 16

Solution    Find the difference between 12 and 16. The difference is 4. Now, check whether the numbers are divisible by the difference. 12 is divisible by 4 and 16 is divisible by 4.Hence, the HCF is 4.

Correct Option(B)

Question. 4 Find HCF of 18 and 22.

Options

(A) 2

(B) 4

(C) 18

(D) 36

Solution     Find the difference between 18 and 22. The difference is 4. Now, check whether the numbers are divisible by the difference. Both 18 and 22 are not divisible by 4. So take the factors of the difference. The factors of 4 are 2*2*1. Now, check whether the numbers are divisible by the factors. 18 and 22 are divisible by factor 2.

Hence, the HCF is 2.

Note: If there are more than two numbers, take the least difference.

Correct Option(A)

Read Also – How to solve HCF questions quickly