НОД (20, 75,130)

To find the greatest common divisor (НОД) of 20, 75, and 130, we can use the Euclidean algorithm.

1. We start by finding the GCD of the first two numbers, 20 and 75: GCD(20, 75) = GCD(75, 20) = ...

   75 ÷ 20 = 3 remainder 15 Now we have the equation: 75 = 3(20) + 15

   We repeat the process with the remainder and the previous divisor: GCD(20, 75) = GCD(20, 15) = ...

   20 ÷ 15 = 1 remainder 5 Now we have the equation: 20 = 1(15) + 5

   We repeat the process once again: GCD(20, 15) = GCD(15, 5) = ...

   15 ÷ 5 = 3 remainder 0 Now we have the equation: 15 = 3(5) + 0

   Since the remainder is 0, we stop here. The GCD of 20 and 75 is 5.

2. Now we find the GCD of the result from step 1 (5) and 130: GCD(5, 130) = GCD(130, 5) = ...

   130 ÷ 5 = 26 remainder 0 Now we have the equation: 130 = 26(5) + 0

   Since the remainder is 0, we stop here. The GCD of 5 and 130 is 5.

Therefore, the greatest common divisor (НОД) of 20, 75, and 130 is 5.