Deep has 825 red candies and Maya has 675 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row?
Deep has 825 red candies and Maya has 675 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row? Correct Answer 75
Concept:
Euclid's division lemma: Given positive integers a and b there exist whole numbers q and r satisfying,
a = bq + r, where, 0 ≤ r ≤ b
Where a = dividend, b = divisor, q = quotient and r = remainder.
Calculation:
In order to find the greatest number of candies that can be arranged in equal rows, we find the HCF of 825 and 675.
Clearly, 825 > 675. Using Euclid's division lemma,
825 = 675 × 1 + 150
⇒ 150 = 75 × 2 + 0
Since, remainder is zero.
∴ HCF (825, 675) = 75
Hence, the greatest number of candies that can be arranged in each row is 75.