Question

the euclidean algorithm

1. use the euclidean algorithm to find the greatest common factor of 840 and 660.

Explanation:

Step1: Apply Euclidean algorithm (divide larger by smaller)

Divide 840 by 660: \( 840 = 660 \times 1 + 180 \)

Step2: Divide previous divisor by remainder

Divide 660 by 180: \( 660 = 180 \times 3 + 120 \)

Step3: Repeat the process

Divide 180 by 120: \( 180 = 120 \times 1 + 60 \)

Step4: Repeat again

Divide 120 by 60: \( 120 = 60 \times 2 + 0 \)
When the remainder is 0, the divisor (60) is the GCF.

Answer:

The greatest common factor of 840 and 660 is 60.