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.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}525 =& 3\cdot5\cdot5\cdot7\\[8pt]619 =& 619\\[8pt]1766 =& 2\cdot883\\[8pt]2400 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\\[8pt]2510 =& 2\cdot5\cdot251\\[8pt]4291 =& 7\cdot613\\[8pt]4296 =& 2\cdot2\cdot2\cdot3\cdot179\\[8pt]4316 =& 2\cdot2\cdot13\cdot83\\[8pt]4393 =& 23\cdot191\\[8pt]5272 =& 2\cdot2\cdot2\cdot659\\[8pt]5383 =& 7\cdot769\\[8pt]6120 =& 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot17\\[8pt]6262 =& 2\cdot31\cdot101\\[8pt]6340 =& 2\cdot2\cdot5\cdot317\\[8pt]7550 =& 2\cdot5\cdot5\cdot151\\[8pt]7827 =& 3\cdot2609\\[8pt]8052 =& 2\cdot2\cdot3\cdot11\cdot61\\[8pt]9880 =& 2\cdot2\cdot2\cdot5\cdot13\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 525, 619, 1766, 2400, 2510, 4291, 4296, 4316, 4393, 5272, 5383, 6120, 6262, 6340, 7550, 7827, 8052 and 9880. )

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

$$\begin{aligned}525 =& 3\cdot5\cdot5\cdot7\\[8pt]619 =& 619\\[8pt]1766 =& 2\cdot883\\[8pt]2400 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\\[8pt]2510 =& 2\cdot5\cdot251\\[8pt]4291 =& 7\cdot613\\[8pt]4296 =& 2\cdot2\cdot2\cdot3\cdot179\\[8pt]4316 =& 2\cdot2\cdot13\cdot83\\[8pt]4393 =& 23\cdot191\\[8pt]5272 =& 2\cdot2\cdot2\cdot659\\[8pt]5383 =& 7\cdot769\\[8pt]6120 =& 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot17\\[8pt]6262 =& 2\cdot31\cdot101\\[8pt]6340 =& 2\cdot2\cdot5\cdot317\\[8pt]7550 =& 2\cdot5\cdot5\cdot151\\[8pt]7827 =& 3\cdot2609\\[8pt]8052 =& 2\cdot2\cdot3\cdot11\cdot61\\[8pt]9880 =& 2\cdot2\cdot2\cdot5\cdot13\cdot19\\[8pt]\end{aligned}$$

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 $~\color{blue}{ \text{GCD = 1} } $.

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