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?
The one-digit factors of 54 are 1,2,3,6,9
so, which three of those add to 14?
write smalles 3 digit number
To solve this problem, we need to find a 3-digit number where the sum of its digits is 14 and the product of its digits is 54. The digits must also be in descending order.
Let's break down the problem step by step:
Step 1: Find the factors of 54
The product of the digits is 54. So, we need to find two factors of 54 that have a sum of 14. The factors of 54 are:
1, 2, 3, 6, 9, 18, 27, 54
Step 2: Determine the possible combinations
Since the digits are in descending order, we can try different combinations of the factors to see if any of them provide the sum of 14.
From the factors above, one possible combination is 9 and 6, since 9 + 6 = 15.
Step 3: Arrange the digits in descending order
Since the digits must be arranged in descending order, the possible number would start with 9.
We have 9 and 6 as two of the digits, which means the last digit must be the remaining factor. In this case, the remaining factor is 1.
So, the possible number is 961.
Step 4: Verify if the digits are all different
Finally, we need to check if all the digits are different in our possible number. In this case, all the digits (9, 6, 1) are different.
Therefore, Shana's number is 961.