Question

Find Greatest Common Divisor of 525, 619, 1766, 2400, 2510, 4291, 4296, 4316, 4393, 5272, 5383, 6120, 6262, 6340, 7550, 7827, 8052 and 9880, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

525 = 619 = 1766 = 2400 = 2510 = 4291 = 4296 = 4316 = 4393 = 5272 = 5383 = 6120 = 6262 = 6340 = 7550 = 7827 = 8052 = 9880 = 3 \cdot 5 \cdot 5 \cdot 7 619 2 \cdot 883 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 2 \cdot 5 \cdot 251 7 \cdot 613 2 \cdot 2 \cdot 2 \cdot 3 \cdot 179 2 \cdot 2 \cdot 13 \cdot 83 23 \cdot 191 2 \cdot 2 \cdot 2 \cdot 659 7 \cdot 769 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 17 2 \cdot 31 \cdot 101 2 \cdot 2 \cdot 5 \cdot 317 2 \cdot 5 \cdot 5 \cdot 151 3 \cdot 2609 2 \cdot 2 \cdot 3 \cdot 11 \cdot 61 2 \cdot 2 \cdot 2 \cdot 5 \cdot 13 \cdot 19

Step 2 : Put a box around factors that are common for all numbers:

525 = 619 = 1766 = 2400 = 2510 = 4291 = 4296 = 4316 = 4393 = 5272 = 5383 = 6120 = 6262 = 6340 = 7550 = 7827 = 8052 = 9880 = 3 \cdot 5 \cdot 5 \cdot 7 619 2 \cdot 883 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 2 \cdot 5 \cdot 251 7 \cdot 613 2 \cdot 2 \cdot 2 \cdot 3 \cdot 179 2 \cdot 2 \cdot 13 \cdot 83 23 \cdot 191 2 \cdot 2 \cdot 2 \cdot 659 7 \cdot 769 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 17 2 \cdot 31 \cdot 101 2 \cdot 2 \cdot 5 \cdot 317 2 \cdot 5 \cdot 5 \cdot 151 3 \cdot 2609 2 \cdot 2 \cdot 3 \cdot 11 \cdot 61 2 \cdot 2 \cdot 2 \cdot 5 \cdot 13 \cdot 19

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $GCD = 1$ .

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