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 the sides of whole number length?
What is the largest number that can be divided into both 70 and 525 with no remainder? Since 525 ends in 5, the side must end in 5.
35
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To find the largest possible square plot with whole number sides that can be divided from a field measuring 70 feet by 525 feet, we need to find the greatest common divisor (GCD) of the two dimensions.
The GCD is the largest number that divides both dimensions without leaving a remainder. In this case, the dimensions are 70 feet and 525 feet.
To find the GCD, we can use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number and using the remainder until we obtain a remainder of zero. Then, the divisor from the previous step is the GCD.
Let's calculate the GCD of 70 and 525:
525 ÷ 70 = 7 with a remainder of 35
70 ÷ 35 = 2 with no remainder
35 ÷ 2 = 17 with a remainder of 1
2 ÷ 1 = 2 with no remainder
1 ÷ 0 = 0
The last divisor with no remainder is 2, which means the GCD of 70 and 525 is 2.
Now, we can divide both dimensions of the field by the GCD to obtain the dimensions of the largest possible square plot:
70 ÷ 2 = 35 feet
525 ÷ 2 = 262.5 feet
Therefore, the largest possible square plot with whole number sides that can be divided from the field measuring 70 feet by 525 feet has sides measuring 35 feet by 262.5 feet.