# HCF Tips and Tricks and Shortcuts

## Tips and Tricks of HCF Questions

This page is all about Tips, Tricks and shortcuts of HCF Questions. You will also get to know about its definition and methods to solve it.
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.

## HCF – Tips, 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.

### Methods to find HCF

• Prime factorization method :

One of the simplest methods to calculate the HCF of a number. The following steps help to calculate HCF of a number.
a) Expand the given number as the product of their prime factors.

b) Check for common prime

• Division Method :
Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

### How to calculate HCF for Fractions :

$HCF of fraction = \frac{HCF of Numerators}{LCM of Denominators}$

Example :

Find out HCF of 3/5, 9/15, 18/25

HCF = HCF of Numerators / LCM of Denominators

HCF of 3, 9 and 18 = 3
LCM of 5, 15 and 25 = 75

HCF of fraction = 3/75

### How to calculate HCF for Decimals

Step 1 : Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.

Step 2 : Now find the LCM/HCF of these numbers without decimal.

Step 3 : Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers

### Question and Answer with solution

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

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

Question 3 : Find the HCF of .63, 1.05, 2.1

Options:

A. .32

B. .21

C. .12

D. .65

Solution : the numbers can be written as .63, 1.05, 2.10

Now find the HCF of these number without decimal.

HCF of 63, 105 and 210 = 21

we need to put decimal point in the result obtained in step 2 leaving two digits on its right.

HCF (.63, 1.05, 2.1) = .21

Question 4 : For any integer n, what is HCF (22n + 7, 33n + 10) equal to?

A. n

B. 1

C. 11

D. None of these

Solution :

HCF of (22n + 7, 33n + 10) is always 1.

On placing different values in the given equation; n = 1, 2, 3, ……

We get,

For n = 1, HCF (22n + 7, 33n + 10) = (29, 43) ⇒ HCF = 1

For n = 2, HCF (22n + 7, 33n + 10) = (51, 76) ⇒ HCF = 1

For n = 3, HCF (22n + 7, 33n + 10) = (73, 109) ⇒ HCF = 1.

Question 5 : The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case is

A. 64

B. 124

C.128

D. 132

Solution :

Required number = HCF of (1356 – 12) , (1868 – 12 ), (2764 – 12)

HCF of 1344, 1856 and 2752 = 64.

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