Find the largest positive integer that leaves the same remainder when divided into each of 889, 961, 1009, and 1189
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hi am gabby and i am 10 years old i dont understand what is the greatest number which when divided into 12500 and 1000 leaves remainders of of 26 and 28
To find the largest positive integer that leaves the same remainder when divided into each of the given numbers, we need to find the common remainder.
Let's start by subtracting two pairs of numbers and examine the remainder of the difference. We subtract 889 from 961:
961 - 889 = 72
Now we subtract 1009 from 1189:
1189 - 1009 = 180
Observe that both differences, 72 and 180, have the same remainder when divided by the unknown integer. This remainder is what we are looking for.
To find the common remainder, we need to find the greatest common divisor (GCD) of 72 and 180.
Using the Euclidean algorithm, we divide the larger number, 180, by the smaller number, 72:
180 ÷ 72 = 2 remainder 36
Next, we divide the smaller number, 72, by the remainder, 36:
72 ÷ 36 = 2 remainder 0
Since we obtained a remainder of 0, the division process ends. The greatest common divisor of 72 and 180 is the remainder at this step, which is 36.
Therefore, the largest positive integer that leaves the same remainder when divided into each of 889, 961, 1009, and 1189 is 36.