Question

Найти нод 432 468 540 с решением

Answer 1

НОД=36
432=2*2*2*2*3*3*3
468=2*2*3*3*13
540=2*2*3*3*3*5
2*2*3*3=36

Answer 2

Finding the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) of the numbers 432, 468, and 540, we can use the Euclidean algorithm. The Euclidean algorithm is an efficient method for finding the GCD of two numbers, and it can be extended to find the GCD of multiple numbers.

The Euclidean algorithm states that the GCD of two numbers is equal to the GCD of the remainder when the larger number is divided by the smaller number. We can apply this algorithm iteratively to find the GCD of multiple numbers.

Let's apply the Euclidean algorithm to find the GCD of 432, 468, and 540:

1. Find the GCD of 432 and 468: - Divide 468 by 432: 468 ÷ 432 = 1 with a remainder of 36. - The GCD of 432 and 468 is equal to the GCD of 432 and 36.

2. Find the GCD of 432 and 36: - Divide 432 by 36: 432 ÷ 36 = 12 with no remainder. - The GCD of 432 and 36 is equal to 36.

So, the GCD of 432, 468, and 540 is 36.

Solution:

The greatest common divisor (GCD) of 432, 468, and 540 is 36.