# Tips-And-Tricks-And-Shortcuts To Solve 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.

## HCF and Tricks and Shortcuts and Tips

• 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

### Ques 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

1. 600
2. 460
3. 800
4. 1400

#### Solution:

The numbers are 40 * 15 and 40 * 20

40 * 15 = 600

40 * 20 = 800

## Type 2: Tips and Tricks and Shortcuts To Find HCF

### Ques 2.

Find the HCF of 3/10, 4/7, 6/5, and 2/9
Options

1. 1/630
2. 3/560
3. 2/543
4. 630

#### Solution

We know that

HCF = HCF of Numerator/LCM of Denominators

HCF = HCF (3, 4, 6, 2)/ LCM (10, 7, 6, 9)

HCF = 1/630 ## Tips and Tricks and Shortcuts to find HCF easily

### Ques. 3

Find HCF of 12 and 16.

Options

(A) 5
(B) 4
(C) 12
(D) 16

#### Correct Option(B)

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.

### Ques. 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.