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H.C.F

Theory and Formula


Question

Q1. Product of two numbers is 4107, and HCF is 37. so find the largest number.

(a) 211 (b) 111 (c) 140 (d) 191

Solution.
HCF (37) divides both the numbers exactly , so we can write

37x . 37y = 4107

xy = 3 (x and y both are prime numbers)

x = 1, y = 3 or y = 1, x = 3

largest number is 37 x 3 = 111
Solution

Q2. what is the greatest number that will divide 38,45 and 52 and will leave as remember 2,3 and 4 respectively.

(a) 2 (b) 3 (c) 4 (d) 6

Solution.
In this case we have to find HCF, as HCF will divide exactly (38 - 2)(45 - 3) and (52 - 4).

Prime factors of 36 = 22 x 32

42 = 21 x 31 x 71 , 48 = 24 x 31

HCF = 2 x 3 = 6
Solution

Q3. The LCM of two numbers is 520 and their HCF is 4.If one of the number is 52, then the other number is.
(a)40 (b)42 (c)50 (d) 52

Solution.
First number x second number= HCF x LCM
52 x second number= 4 x 520
second number = (4 x 520)/52 = 40
Solution

Q4. Find the greatest number that will divide 360 and 650 and will leave as remainder 6 and 1 respectively .

Solution.
The greatest number will be the HCF of (360 - 6) and (650 - 1).
So, HCF of 354 and 649 is 59 .
Solution

Q5. Find the H.C.F of 20x2 y9 z, 16x5 y3, 12x3 y10
(a) 4x2 y3 (b) 2xy (c) 2 (d) 1

Solution.
H.C.F of 20, 16, 12 = 4
Highest power of x common to all = x2
Highest power of y common to all = y3
z is not common so omit it
HCF is 4x2 y3
Solution

Q6. Find the HCF of 144, 180, and 192 .

Solution.
HCF = 12 .
Solution

Q7. HCF and LCM of two number are 21 & 84. the ratio of two numbers are 1;4 . Find the smallest number.

21 x 84 = 4x2

x : 4x (given)

x = 21

or

Direct multiply HCF by ratio

21 x 1 = 21

So, lowest number is 21 .
Solution

Q8. Find the LCM and HCF of 96 and 404.

Solution.
96 = 25 x 3 and 404 = 22 x 101

Least exponents common prime factorisation

HCF = 22 = 4

As we know that .

Product of HCF and LCM = Product of two numbers

4 x (LCM) = 96 x 404

LCM =
404 x 96/4
= 101 x 96 = 9696

HCF = 4 , LCM = 9696
Solution

Q9. Find the HCF of 144, 180, and 192 .

Solution.
HCF = 12 .
Solution

Q10. The LCM of three numbers are 120, which number cannot be HCF of these numbers .
(a) 38 , (b) 8 , (c) 12 , (d) 24

Solution.
38

Note : LCM is divisible by HCF (exactly).
Solution