The greatest number will divide 3026 and 5053 leaving remainder 11 and 13 respectively? The answer should be 45 however as per defence ministery answer is 15. Please provide the correct answer.

Arun
25750 Points
5 years ago
Required Number can be given by:

HCF of (3026 - 11) and (5053 - 13)
HCF of 3015 and 5040 = 15.
To find HCF, we break the given numbers in their prime Factors.
3015 = 3*3*5*67
5040 = 2*2*2*2*3*3*5*7
We take common multiples in these two given numbers to get required HCF.
And Common multiples are: 3*5
So, Required HCF = 15.
Ritvik Choudhary
12 Points
5 years ago
HCF of (3026 - 11) and (5053 - 13)
HCF of 3015 and 5040 = 45
3015)5040(1
3015
====
2025)3015(1
2025
====
990)2025(2
1980
====
45)990(22
990
====
0
Soumendu Majumdar
159 Points
5 years ago
Dear Ritvik,
Given dividends are 3026 and 5053 and their respective remainders are 11 and 13.
So first we need to subtract the remainders from the dividends.
Hence the new dividends are 3015 and 5040.
Now to find the highest number which divides them we need to find the h.c.f of the two.
Since they are large dividends I will break them into their prime factors which will be easier for you.
3015 = 3 x 3 x 5 x 67
5040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
Looking at their factors you will find 3 x 3 x 5 is common to both
Hence H.C.F(3015,5040) = 45
Now I don’t know why the answer would be 15?
It can only be 15 if the question says that you have to exclude multiple common factors!
In this 3 is a factor that is common twice for both 3015 and 5040 so if the question mentions that you have to exclude multiple common factors then the highest number dividing them is 15.
Hope it helps!
regards,
Soumendu Majumdar