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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
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let N be the greatest number that will divide 1305, 4665 and 6905, lea...
N = H.C.F. of (4665 – 1305), (6905 – 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120.
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Let N be the greatest number that will divide 1305, 4665 and 6905, lea...
Solution:
To find the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case, we need to find the difference between any two numbers and then find the HCF of the resulting difference and the smallest number.
Let us consider the difference between 1305 and 4665:
4665 - 1305 = 3360
Now, let us find the HCF of 3360 and 1305:
3360 = 2^5 x 3 x 5 x 7
1305 = 3 x 5 x 29
The common factors are 3 and 5. Therefore, the HCF of 1305 and 3360 is 15.
Now, let us check if 15 leaves the same remainder when divided by 1305, 4665 and 6905.
1305 = 15 x 87
4665 = 15 x 311
6905 = 15 x 460 + 5
As we can see, 15 leaves a remainder of 5 when divided by 6905. Therefore, we need to subtract 5 from 15 to get the required number.
Thus, the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case is 10.
The sum of the digits in 10 is 1 + 0 = 1.
Therefore, the correct answer is option A, 4.
To find the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case, we need to find the difference between any two numbers and then find the HCF of the resulting difference and the smallest number.
Let us consider the difference between 1305 and 4665:
4665 - 1305 = 3360
Now, let us find the HCF of 3360 and 1305:
3360 = 2^5 x 3 x 5 x 7
1305 = 3 x 5 x 29
The common factors are 3 and 5. Therefore, the HCF of 1305 and 3360 is 15.
Now, let us check if 15 leaves the same remainder when divided by 1305, 4665 and 6905.
1305 = 15 x 87
4665 = 15 x 311
6905 = 15 x 460 + 5
As we can see, 15 leaves a remainder of 5 when divided by 6905. Therefore, we need to subtract 5 from 15 to get the required number.
Thus, the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case is 10.
The sum of the digits in 10 is 1 + 0 = 1.
Therefore, the correct answer is option A, 4.
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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)4b)5c)6d)8Correct answer is option 'A'. Can you explain this answer?
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