Question

НОД 232 и 261? НОД 124 и 148 НОД 24,48 и 54

Answer 1

Ответ:

НОД (232 и 261) =29

НОД (124 и 148) =4

НОД (24, 48 и 54) =6

Answer 2

The greatest common divisor (GCD) or НОД of two or more numbers is the largest positive integer that divides all of the given numbers without leaving a remainder. Let's calculate the GCD for the sets of numbers you provided:

1. GCD of 232 and 261: To find the GCD of 232 and 261, you can use the Euclidean algorithm:

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261 = 1 * 232 + 29
232 = 8 * 29 + 20
29 = 1 * 20 + 9
20 = 2 * 9 + 2
9 = 4 * 2 + 1
2 = 2 * 1 + 0

The GCD is 1, since that's the remainder at the last step of the algorithm.

2. GCD of 124 and 148:

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148 = 1 * 124 + 24
124 = 5 * 24 + 4
24 = 6 * 4 + 0

The GCD is 4, which is the last nonzero remainder.

3. GCD of 24, 48, and 54: You can use the Euclidean algorithm to find the GCD of three numbers:

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54 = 1 * 48 + 6
48 = 8 * 6 + 0

The GCD is 6, which is the last nonzero remainder.

So, to summarize:

• GCD(232, 261) = 1
• GCD(124, 148) = 4
• GCD(24, 48, 54) = 6

Answer 3

The greatest common divisor (GCD), also known as the greatest common factor (GCF) or highest common factor (HCF), is the largest positive integer that divides two or more numbers without leaving a remainder. Let's calculate the GCD for the given sets of numbers:

1. GCD of 232 and 261: To find the GCD of 232 and 261, we can use the Euclidean algorithm.

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261 = 1 * 232 + 29
232 = 7 * 29 + 1
29 = 29 * 1 + 0

Since the remainder becomes 0, the GCD is the last non-zero remainder, which is 1. Therefore, GCD(232, 261) = 1.

2. GCD of 124 and 148: Similarly, for 124 and 148:

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148 = 1 * 124 + 24
124 = 5 * 24 + 4
24 = 6 * 4 + 0

The GCD is 4. Therefore, GCD(124, 148) = 4.

3. GCD of 24, 48, and 54: For three numbers, we can apply the algorithm iteratively:

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48 = 2 * 24 + 0
54 = 1 * 48 + 6

The GCD is 6. Therefore, GCD(24, 48, 54) = 6.

To summarize:

• GCD(232, 261) = 1
• GCD(124, 148) = 4
• GCD(24, 48, 54) = 6