Question

На одно и тоже число поделили числа 110 и 161 то получили соответственно остатки 2 и 26 найдите на какое число поделили

Answer 1

Это число 27 решение
110-2=108    161-26=135
оба числа делятся на 27

Answer 2

Solution:

To find the number by which both 110 and 161 were divided to get remainders of 2 and 26 respectively, we can use the following approach:

Let's assume the number we are looking for is denoted by x. Then we can express the given information in the form of congruences:

1. 110 ≡ 2 (mod x) 2. 161 ≡ 26 (mod x)

We can solve these congruences to find the value of x.

First, let's solve the congruence 110 ≡ 2 (mod x):

110 ≡ 2 (mod x)

This means that the difference between 110 and 2 is divisible by x. So, we have:

110 - 2 ≡ 0 (mod x) 108 ≡ 0 (mod x)

Next, let's solve the congruence 161 ≡ 26 (mod x):

161 ≡ 26 (mod x)

This means that the difference between 161 and 26 is divisible by x. So, we have:

161 - 26 ≡ 0 (mod x) 135 ≡ 0 (mod x)

Now, we need to find the common divisor of 108 and 135 to find the value of x.

Calculation:

The common divisors of 108 and 135 are 1, 3, 9, 27.

So, the number by which both 110 and 161 were divided to get remainders of 2 and 26 respectively is 27.

Therefore, x = 27.

This means that both 110 and 161 were divided by 27 to get the given remainders.