Question

Найдите НОД (720; 460).

Answer 1

720|2
360|2
180|2
90|2
45|3
15|3
5|5
720=2⁴×3²×5

460|2
230|2
115|5
23|23
460=2²×5×23
НОД 720 и 460=2²×5=4×5=20

Answer 2

Calculating the Greatest Common Divisor (GCD) of 720 and 460

To find the greatest common divisor (GCD) of 720 and 460, we can use the Euclidean algorithm, which involves finding the remainder of the division of the larger number by the smaller number and then replacing the larger number with the smaller number and the smaller number with the remainder. We continue this process until the remainder is 0, at which point the divisor is the GCD.

Using the Euclidean algorithm: - GCD(720, 460) = GCD(460, 720 % 460) - GCD(460, 260) = GCD(260, 460 % 260) - GCD(260, 200) = GCD(200, 260 % 200) - GCD(200, 60) = GCD(60, 200 % 60) - GCD(60, 20) = GCD(20, 60 % 20) - GCD(20, 0) = 20

So, the GCD of 720 and 460 is 20.