Find the largest number which divides 630 and 940 leaving remainder 6 and 4 respectively
simple method:
numbers which divide by 630 leaving remainder of 6:
636 1266 1896 2526 3156 3786 4416 ...
numbers which divide by 940 leaving remainder of 4:
944 1884 2824 3764 ...... looks hopeless
alternate method
Let that number be k
then
k/630 = x + 6/630 --> k = 630x + 6
k/940 = y + 4/940 --> k = 940y + 4
where both x and y are whole numbers
630x + 6 = 940y + 4
630x - 940y = -2
315x - 470y = -1
470y - 315x = 1
5(94x - 63y) = 1
no way!, the left side is a multiple of 5, and x and y are whole numbers. That left side can never be 1
no such number
Ccgczvzgga@6178182(
Try 12. 630/12=52 R6 and 940/12=78 R4 but is 12 the largest number possible?
Xkvwkvucsu
Amazing!😄👏
To find the largest number that divides 630 and 940 leaving remainders of 6 and 4 respectively, we can use the concept of finding the Greatest Common Divisor (GCD) of two numbers.
Step 1: Find the common factors of 630 and 940:
The factors of 630 are: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.
The factors of 940 are: 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940.
Step 2: Identify the common factors that leave remainders of 6 and 4 respectively:
From the factors listed above, we can see that the common factors that leave a remainder of 6 when divided into 630 are: 6, 42, 126, 210, and 630.
And the common factors that leave a remainder of 4 when divided into 940 are: 4, 20, 188, and 940.
Step 3: Find the largest common factor:
The largest common factor that divides both 630 and 940 leaving remainders of 6 and 4 respectively is the highest number in the intersection of the two sets of common factors.
In this case, the largest common factor is 2.
So, the largest number that divides 630 and 940, leaving remainders of 6 and 4 respectively, is 2.