Question

Find Greatest Common Divisor of 121, 645, 100, 408, 832, 19, 2, 432, 902, 8, 176, 640 and 19, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

121 = 645 = 100 = 408 = 832 = 19 = 2 = 432 = 902 = 8 = 176 = 640 = 19 = 11 \cdot 11 3 \cdot 5 \cdot 43 2 \cdot 2 \cdot 5 \cdot 5 2 \cdot 2 \cdot 2 \cdot 3 \cdot 17 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 13 192 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 11 \cdot 41 2 \cdot 2 \cdot 2 2 \cdot 2 \cdot 2 \cdot 2 \cdot 11 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 19

(view steps on how to factor 121, 645, 100, 408, 832, 19, 2, 432, 902, 8, 176, 640 and 19. )

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

121 = 645 = 100 = 408 = 832 = 19 = 2 = 432 = 902 = 8 = 176 = 640 = 19 = 11 \cdot 11 3 \cdot 5 \cdot 43 2 \cdot 2 \cdot 5 \cdot 5 2 \cdot 2 \cdot 2 \cdot 3 \cdot 17 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 13 192 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 11 \cdot 41 2 \cdot 2 \cdot 2 2 \cdot 2 \cdot 2 \cdot 2 \cdot 11 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 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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