HCF Tips and Tricks and Shortcuts

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.