Question

НОД 48 и 28. 42 и 72. 36 и 63

Answer 1

48 = 2 * 2 * 2 * 2 * 3
28 = 2 * 2 * 7 
НОД ( 48 ; 28 ) = 2 * 2 = 4 
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42 = 2 * 3 * 7 
72 = 2 * 2 * 2 * 3 * 3 
НОД ( 42 ; 72 ) = 2 * 3 = 6 
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36 = 2 * 2 * 3 * 3 
63 = 3 * 3 * 7 
НОД ( 36 ; 63 ) = 3 * 3 = 9

Answer 2

Greatest Common Divisor (GCD) of 48 and 28

To find the greatest common divisor (GCD) of 48 and 28, we can use the Euclidean algorithm. The Euclidean algorithm states that the GCD of two numbers can be found by repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The last non-zero remainder is the GCD of the two numbers.

Let's apply the Euclidean algorithm to find the GCD of 48 and 28:

1. Divide 48 by 28: 48 ÷ 28 = 1 remainder 20 2. Divide 28 by 20: 28 ÷ 20 = 1 remainder 8 3. Divide 20 by 8: 20 ÷ 8 = 2 remainder 4 4. Divide 8 by 4: 8 ÷ 4 = 2 remainder 0

Since the remainder is now zero, the GCD of 48 and 28 is the last non-zero remainder, which is 4.

Therefore, the GCD of 48 and 28 is 4.

Greatest Common Divisor (GCD) of 42 and 72

To find the GCD of 42 and 72, we can again use the Euclidean algorithm:

1. Divide 72 by 42: 72 ÷ 42 = 1 remainder 30 2. Divide 42 by 30: 42 ÷ 30 = 1 remainder 12 3. Divide 30 by 12: 30 ÷ 12 = 2 remainder 6 4. Divide 12 by 6: 12 ÷ 6 = 2 remainder 0

The last non-zero remainder is 6, so the GCD of 42 and 72 is 6.

Greatest Common Divisor (GCD) of 36 and 63

Applying the Euclidean algorithm to find the GCD of 36 and 63:

1. Divide 63 by 36: 63 ÷ 36 = 1 remainder 27 2. Divide 36 by 27: 36 ÷ 27 = 1 remainder 9 3. Divide 27 by 9: 27 ÷ 9 = 3 remainder 0

The last non-zero remainder is 9, so the GCD of 36 and 63 is 9.

In summary, the GCD of: - 48 and 28 is 4 - 42 and 72 is 6 - 36 and 63 is 9.

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