A bakery seller has 210 vanilla pastries and 390 chocolate pastries. She wants to stack them in such a way that each stack has the same number, and they can take up the least area of the tray. What is the number of pastries that can be placed in each stack for this purpose?
Answers & Comments
Answer:
20
Explanation:
No. of stacks = HCF (210, 390) = 30
∴ No. of pastries in each stack = (210 + 390)/30 = 600/30 = 20
Verified answer
Answer:
To find the number of pastries that can be placed in each stack while taking up the least area, you need to find the greatest common divisor (GCD) of 210 and 390.
The GCD of two numbers is the largest positive integer that divides both numbers without a remainder.
The prime factorization of 210 is \(2 x 3 x 5 x 7\).
The prime factorization of 390 is \(2 x 3 x 5 x 13\).
To find the GCD, you take the common prime factors with the lowest exponent in both factorizations and multiply them together. In this case, the common prime factors are 2, 3, and 5. The lowest exponent for each of these primes is 1.
Therefore, the GCD of 210 and 390 is \(2 x 3 x 5 = 30\).
So, the bakery seller can stack the pastries in stacks of 30 to take up the least area on the tray.