What is the minimum and what is the maximum sum of 7 numbers which product is equal to 30?
Teacher tip
Suitable for exercising the factorization of numbers.Solution
These are all representations of the number 30 as a product of 7 numbers:
\(30 = 30 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 15 \cdot 2 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 10 \cdot 3 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 5 \cdot 6 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 5 \cdot 3 \cdot 2 \cdot 1 \cdot 1 \cdot 1 \cdot 1.\)
The minimum sum is \(5 + 3 + 2 + 1 + 1 + 1 + 1 = 14\), and the maximum sum is \(30 + 1 + 1 + 1 + 1 + 1 + 1 = 36\).
\(30 = 30 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 15 \cdot 2 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 10 \cdot 3 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 5 \cdot 6 \cdot 1 \cdot 1 \cdot 1 \cdot 1 \cdot 1,\)
\(30 = 5 \cdot 3 \cdot 2 \cdot 1 \cdot 1 \cdot 1 \cdot 1.\)
The minimum sum is \(5 + 3 + 2 + 1 + 1 + 1 + 1 = 14\), and the maximum sum is \(30 + 1 + 1 + 1 + 1 + 1 + 1 = 36\).
Additional question
Can you find the minimum and the maximum product of 7 numbers which sum is equal to 30?
14/18
ReplyDeleteThe minimum sum is 14 (=5+3+2+1+1+1+1), but the maximum sum is much more higher than 18.
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