Find the GCD (greatest common denominator) of all three-digit numbers written using the numbers 3
| April 4, 2021 | education
Find the GCD (greatest common denominator) of all three-digit numbers written using the numbers 3, 6 and 9 without repetitions.
The resulting three-digit numbers from the given digits 3,6 and 9: 369,693,396,639,963,936. We decompose these numbers into prime factors: 369 = 3 * 3 * 41, 693 = 3 * 3 * 7 * 11, 396 = 2 * 2 * 3 * 3 * 11, 639 = 3 * 3 * 71, 963 = 3 * 3 * 107, 936 = 2 * 2 * 2 * 3 * 3 * 13. The greatest common divisor of these GCD numbers (369,693,396,639,963,936) = 3 * 3 = 9.
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