k is the greatest number that divides 2996, 4752 and 7825 leaving the remainder in each case equal. Find the product of the marks of K.
no idea what are "the marks of K"
I have this rather simple simulation app of a computer language we used in the 70s and 80s called BASIC.
I made up a rather dinky and simple program consisting of 6 lines:
10 for k = 2 to 4752
20 r1 = 2996-int(2996/k)*k
30 r2 = 4752-int(4752/k)*k
40 r3 = 7825-int(7825/k)*k
50 if ((r1 = r2) and (r1 = r3)) then print k,r1
60 next k
439 362
It told me that the greatest number that divides 2996, 4752 and 7825 leaving the remainder in each case equal
is 439 and the remainder in each case is 362
So k = 439 , rem = 362
e.g.
2996/439 = 6 with remainder of 362
4752/439 = 10 with remainder of 362
7825/439 =17 with remainder of 362
Don't know what you mean by "the product of the marks of K
Take it from there
Thanks for the entertaining question. I know this can be done by
modular arithmetic, but I haven't done that in over 60 years.
Sorry dear
Didn't understand any step
To find the greatest number, k, that divides three given numbers and leaves the same remainder in each case, we need to find the common remainder of these numbers when divided by k.
1. Find the remainders:
- Divide 2996 by k and note the remainder r1.
- Divide 4752 by k and note the remainder r2.
- Divide 7825 by k and note the remainder r3.
2. Set up equations:
- r1 = r2 = r3
3. Perform division and find common remainder:
- Identify the factors of the given numbers and their respective remainders to determine the value of k.
For example, let's find the remainders for each given number:
- 2996 divided by k gives the remainder r1.
- 4752 divided by k gives the remainder r2.
- 7825 divided by k gives the remainder r3.
4. Determine the values of k:
- Find the greatest common divisor (GCD) of the differences between the remainders. In this case, the GCD of (r1-r2), (r2-r3), and (r3-r1) will give us the value of k.
For example, if we find that (r1 - r2) = 0, (r2 - r3) = 0, (r3 - r1) = 0, then k will be equal to these remainders.
5. Calculate the product of the values of k:
- Once you have determined the value(s) of k, multiply them together to find the product of k.
Once you have found the value(s) of k, you can multiply them together to find the product of k.