If you multiply 6 by an even number, the answer will end with the same digit. The number in the ten's place will be half of the number in the one's place. What are the factors and their product?
the same digit --- as what? The 6?
In that case, the even number is ending in 6
so the product ends in 36
not sure what else you're after.
Let's start by finding all the even numbers that meet the given conditions.
The number in the ten's place will be half of the number in the one's place. This means that the possible digits for the units place are 0, 2, 4, 6, and 8.
Next, we want to find a number in which the product of 6 and the digit in the units place results in a number that ends in the same digit.
Let's go through the possible digits one by one:
1. If the digit in the units place is 0, then the product of 6 and 0 is 0, which does not end in 0.
2. If the digit in the units place is 2, then the product of 6 and 2 is 12, which ends in 2. Also, the digit in the tens place is half of 2, which is 1.
3. If the digit in the units place is 4, then the product of 6 and 4 is 24, which ends in 4. Also, the digit in the tens place is half of 4, which is 2.
4. If the digit in the units place is 6, then the product of 6 and 6 is 36, which ends in 6. Also, the digit in the tens place is half of 6, which is 3.
5. If the digit in the units place is 8, then the product of 6 and 8 is 48, which ends in 8. Also, the digit in the tens place is half of 8, which is 4.
Therefore, the factors and their product are:
- 6 * 2 = 12
- 6 * 4 = 24
- 6 * 6 = 36
- 6 * 8 = 48
So, the factors and their product are (2, 12), (4, 24), (6, 36), and (8, 48).
To determine the factors and their product that satisfy the given condition, we can start by finding the possible even numbers that satisfy the second rule: the number in the ten's place must be half of the number in the one's place.
We can list down the possible even one's place digits and their corresponding ten's place digits:
- 0 in the one's place would result in 0 in the ten's place, which is not an option since the ten's place cannot be zero.
- 2 in the one's place would result in 1 in the ten's place (half of 2).
- 4 in the one's place would result in 2 in the ten's place (half of 4).
- 6 in the one's place would result in 3 in the ten's place (half of 6).
- 8 in the one's place would result in 4 in the ten's place (half of 8).
Now that we have determined the possible two-digit factors, we can find their product.
Let's multiply each possible two-digit factor by 6:
- 6 multiplied by 12 equals 72.
- 6 multiplied by 24 equals 144.
- 6 multiplied by 36 equals 216.
- 6 multiplied by 48 equals 288.
Therefore, the factors that satisfy both conditions, and their product, are:
- 12 and 72
- 24 and 144
- 36 and 216
- 48 and 288.