Tips and Tricks and Shortcuts of HCF Questions

May 29, 2023

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

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