A large field measures 70 feet by 525 feet. If you divide it up into equal square garden plots, what size would the largest possible plot be with sides of whole number length?​

9514 1404 393

  35 feet square

Step-by-step explanation:

The greatest common factor of 70 and 525 is 35. The largest square plot can be 35 feet on a side.

  70 = 2·35

  525 = 15·35

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I like to find the GCD (greatest common divisor) using Euclid's algorithm. We find the remainder when dividing the larger by the smaller. When that remainder is not zero, we replace the larger number with the remainder, and repeat. When the remainder is zero, the divisor is the GCD.

  525/70 = 7 r 35

  70/35 = 2 r 0 . . . . . 35 is the GCD