I am thinking of a three-digit number. It is an odd multiple of three, and the product of its digits is 24. It is larger than 15 squared. What are all the numbers that I could be thinking of?
969? or 699?
Sra
product of digits (not sum) is 24
so, 2*2*6 or 2*3*4
423 = 3 * 141
Number must be odd to be on add multiple of 3
not sure help
NO. it is 269,817, 245, and 821....
To find the possible numbers, we need to consider the given criteria:
1. An odd multiple of three: The first digit must be odd, and the sum of all three digits must be a multiple of three.
2. The product of its digits is 24: We need to find all sets of three digits whose product is 24.
3. Larger than 15 squared (15² = 225): The number must be greater than 225.
Let's break it down step by step:
1. Finding sets of three digits whose product is 24:
The possible sets of digits whose product is 24 are {1, 2, 12}, {1, 3, 8}, {1, 4, 6}, {2, 2, 6}, and {2, 3, 4}.
2. The first digit must be odd and the sum of all three digits must be a multiple of three:
Considering the first condition, the first digit can be either 1, 3, or 9.
For each possible first digit, let's calculate the sum of the three digits:
a) First digit = 1: The possible sets are {1, 2, 12} and {1, 3, 8}.
The sum of the digits for {1, 2, 12}: 1 + 2 + 12 = 15. Not a multiple of three.
The sum of the digits for {1, 3, 8}: 1 + 3 + 8 = 12. A multiple of three.
b) First digit = 3: The possible set is {3, 4, 6}.
The sum of the digits: 3 + 4 + 6 = 13. Not a multiple of three.
c) First digit = 9: The possible sets are {9, 2, 2}, {9, 3, 4}, and {9, 1, 4}.
The sum of the digits for {9, 2, 2}: 9 + 2 + 2 = 13. Not a multiple of three.
The sum of the digits for {9, 3, 4}: 9 + 3 + 4 = 16. Not a multiple of three.
The sum of the digits for {9, 1, 4}: 9 + 1 + 4 = 14. Not a multiple of three.
Based on the above calculations, the only set that satisfies all the conditions is {1, 3, 8}.
Thus, the only possible number you could be thinking of is 138.