Question

Как найти НОД (24,48) , НОД (62,31) , НОД (132,11) , НОД (256, 32) , НОД (45,15) , НОД (21,63) ПОМОГИТЕ ПОЖАЛУЙСТА)

Answer 1

НОД 48 и 24 = 24 НОД 62 и 31 = 31 НОД 132 и 11 = 11 НОД 256 и 32 = 32 НОД 45 и 15 = 15 НОД 21 и 63 = 21

Answer 2

Finding the Greatest Common Divisor (GCD)

To find the Greatest Common Divisor (GCD) of the given numbers, we can use the Euclidean algorithm, which is based on the principle that the GCD of two numbers does not change if the larger number is replaced by its difference with the smaller number. Let's calculate the GCD for each pair of numbers:

1. GCD(24, 48): - Using the Euclidean algorithm: - GCD(24, 48) = GCD(48, 24) = 24 - Therefore, GCD(24, 48) = 24.

2. GCD(62, 31): - Using the Euclidean algorithm: - GCD(62, 31) = GCD(31, 62) = 31 - Therefore, GCD(62, 31) = 31.

3. GCD(132, 11): - Using the Euclidean algorithm: - GCD(132, 11) = GCD(11, 132) = 11 - Therefore, GCD(132, 11) = 11.

4. GCD(256, 32): - Using the Euclidean algorithm: - GCD(256, 32) = GCD(32, 256) = 32 - Therefore, GCD(256, 32) = 32.

5. GCD(45, 15): - Using the Euclidean algorithm: - GCD(45, 15) = GCD(15, 45) = 15 - Therefore, GCD(45, 15) = 15.

6. GCD(21, 63): - Using the Euclidean algorithm: - GCD(21, 63) = GCD(63, 21) = 21 - Therefore, GCD(21, 63) = 21.

In summary, the Greatest Common Divisors (GCDs) for the given pairs of numbers are: - GCD(24, 48) = 24 - GCD(62, 31) = 31 - GCD(132, 11) = 11 - GCD(256, 32) = 32 - GCD(45, 15) = 15 - GCD(21, 63) = 21