Question

Find Greatest Common Divisor of 951, 744, 516, 487, 808, 808, 676, 328, 940 and 470, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

951 = 744 = 516 = 487 = 808 = 808 = 676 = 328 = 940 = 470 = 3 \cdot 317 2 \cdot 2 \cdot 2 \cdot 3 \cdot 31 2 \cdot 2 \cdot 3 \cdot 43 487 2 \cdot 2 \cdot 2 \cdot 101 2 \cdot 2 \cdot 2 \cdot 101 2 \cdot 2 \cdot 13 \cdot 13 2 \cdot 2 \cdot 2 \cdot 41 2 \cdot 2 \cdot 5 \cdot 47 2 \cdot 5 \cdot 47

(view steps on how to factor 951, 744, 516, 487, 808, 808, 676, 328, 940 and 470. )

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

951 = 744 = 516 = 487 = 808 = 808 = 676 = 328 = 940 = 470 = 3 \cdot 317 2 \cdot 2 \cdot 2 \cdot 3 \cdot 31 2 \cdot 2 \cdot 3 \cdot 43 487 2 \cdot 2 \cdot 2 \cdot 101 2 \cdot 2 \cdot 2 \cdot 101 2 \cdot 2 \cdot 13 \cdot 13 2 \cdot 2 \cdot 2 \cdot 41 2 \cdot 2 \cdot 5 \cdot 47 2 \cdot 5 \cdot 47

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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