Shana has written a 3 digit number in which the digits are all different.
The sum of the digit of her number is 14.
And the product of her number is 54.
The digits are in order from greatest to least.
What are her numbers?
you have to find other site this one is trash
one-digit factors of 54 are 1,2,3,6,9
To find Shana's numbers, we can use a systematic approach by considering the information given.
We know that Shana's number is a 3-digit number in which the digits are all different. Let's call the digits a, b, and c.
1. The sum of the digits is 14.
This means that a + b + c = 14.
2. The product of the digits is 54.
This means that a * b * c = 54.
3. The digits are in order from greatest to least.
This implies that a > b > c.
Using these conditions, we can explore different combinations of numbers until we find a solution.
Since the digits are different, we can assume that the first digit (a) cannot be 1, 2, or 3 because these values alone would not yield a sum of 14 and a product of 54.
Let's start exploring the possible values for a:
If a is 4, then b + c = 10, and b * c = 54. Possible combinations are (5, 9) or (6, 8). However, none of these combinations give a sum of 14, so this is not a solution.
If a is 5, then b + c = 9, and b * c = 54. The only possible combination is (6, 3), as no other combination satisfies both conditions. Therefore, one possible number is 563.
If a is 6, then b + c = 8, and b * c = 54. The only possible combination is (7, 1), as no other combination satisfies both conditions. However, since the digits cannot be repeated, this is not a solution.
Thus, the only possible number that satisfies both conditions is 563. Therefore, Shana's number is 563.