# Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

1. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
A. 4
B. 5
C. 6
D. 8
Explanation:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
2. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A. 9000
B. 9400
C. 9600
D. 9800
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
3. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
A. 101
B. 107
C. 111
D. 185
Explanation:
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
4. Find the HCF of 2X 5X 7X 112, 7X 5X 2X 13, 5X 2X 7X 17.
For this question we need to take common factors first, and then lowest powers.
Here common factors are 2, 5, 7.
Then write their lowest powers.
Answer = 22 x 5x 73.
5. Find the LCM of 2X 5X 7X 112, 7X 5X 2X 13, 5X 2X 7X 17.
For this question we need to write all the given numbers , and then write their Highest powers.
All the numbers are 2, 5, 7, 11, 13, 17.
Then write their Highest powers.
Answer = 27 x 5x 7x 11x 13 x 17.

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