HCF and LCM Quiz 1

Explanation:

Required number = H.C.F. of (1657 - 6) and (2040 - 8)

= H.C.F. of 1651 and 2032 = 127.

Explanation:

Since 753xy is divisible by 5 as well as 2, so y = 0.

Now, 753x0 must be divisible by 9.

So sum of digits must be divisible by 9

7+5+3+x+0 = 15+x

Now 15+x should be divisible by 9 if we take x = 3

Then, 15+3 = 18 which is divisible by 9

Which means x is 3

x + y = (3 + 0) = 3.

Explanation:

Let the required numbers be 33a and 33b. Where a,b are coprime.

Then 33a +33b= 528   =>   a+b = 16.

Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).

Therefore, Required numbers are  ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4

Explanation:

Let a and b are the numbers.Then a+b is 70 and ab is 1221.

a = 70 - b…... (i)

ab = 1221

(70-b)b = 1221

70b-b2-1221 = 0

Multiplying the above equation by (-1)

Then, the equation becomes: b2 - 70b + 1221 = 0

Solving the above equation we get through the middle term splitting method

b = 37

Substituting the value of b in equation (i) a = 33

Explanation:

Product of numbers = 11 x 385 = 4235

Let the numbers be 11a and 11b . Then , 11a x 11b = 4235  =>  ab = 35

Now, co-primes with product  35 are (1,35) and (5,7)

So, the numbers are ( 11 x 1, 11 x 35)  and (11 x 5, 11 x 7)

Since one number lies 75 and 125, the suitable pair is  (55,77)

Hence , required number = 77

Explanation:

LCM of 2, 3, 7 is 42.

=> (777 – 333)/42 =10.57 => 10 Numbers.

Explanation:

Let the numbers be x and 4x. Then,

X * 4x = 84 *21 = x^2 = 84 x 21 / 4

=>x = 21

Hence Larger Number = 4x = 84

Explanation:

The sum five consecutive integers can be written as n + (n + 1) + (n + 2)+(n+3)+(n+4) = 5n + 10

If the sum is 24, we need to solve the equation 5n+10 = 215;

=> 5n = 205;

=> n = 41

The greatest of 5 consecutive integers is n+4 = 41+4 = 45

Explanation:

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.

Explanation:

By dividing 10575 with 115

We get remainder  = 110

So the nearest number is 10575 - 110 = 10465