the product of six whole numbers is 36. What is the least possible value of their sum?
I assume that some of the numbers can be the same, otherwise the least possible multiplication would be
1x2x3x4x5x6 = 720
so to get 36 using the smallest possible numbers would be
1x1x2x2x3x3
and the least possible sum = 15
fake answer. wasting of time.. use less
To find the least possible value of the sum, we need to consider the factors of 36. The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36
Since the product of six whole numbers is 36, we need to find combinations of these factors that would give us six numbers when multiplied together.
Let's consider the prime factorization of 36: 2^2 * 3^2.
So, one possible combination would be: 2 * 2 * 3 * 1 * 1 * 1 = 12.
Now, we need to find another combination that would give us six numbers when multiplied together and has a smaller sum.
Let's say we use the factors 1, 3, 3, 1, 1, and 1:
1 * 3 * 3 * 1 * 1 * 1 = 9
Therefore, the least possible value of their sum is 12 + 9 = 21.
To find the least possible value of the sum of six whole numbers given their product, we need to determine the factors of 36 and find the combination that minimizes the sum.
Step 1: Find the Factors of 36
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: Determine Combinations
To find the combination that minimizes the sum, we need to consider pairs of factors that multiply to 36. Since there are six numbers, we can consider combinations of two, three, or four numbers.
Pairs: We can have a combination of two numbers, giving us (1, 36), (2, 18), (3, 12), or (4, 9).
Triplets: We can have a combination of three numbers, giving us (1, 2, 18), (1, 3, 12), (1, 4, 9), (2, 3, 6).
Quartets: We can have a combination of four numbers, giving us (1, 2, 3, 6).
Step 3: Calculate the Sum
Next, we calculate the sums for each combination:
Pairs: (1+36), (2+18), (3+12), (4+9)
Triplets: (1+2+18), (1+3+12), (1+4+9), (2+3+6)
Quartets: (1+2+3+6)
Step 4: Find the Minimum Sum
We compare each sum and find the minimum:
Pairs: 37, 20, 15, 13
Triplets: 21, 16, 14, 11
Quartets: 12
From these calculations, we can see that the minimum sum is 11, which occurs with the combination (2, 3, 6).