What number do I multiply by to give me 1,428 outof 1,2,6, and8.
Divide 1,428 by each of those numbers. What do you get?
There are some short cuts:
1 will always work
since the number is even (ends in 8)
the number is divisible by 2.
If the sum of the digits is divisible by 3 then the number is divisible by 3.
If the number is divisible by 2 and 3 then it is divisible by 6.
To find the number you need to multiply by to give you 1,428, you can use a simple approach called trial and error. Here's how you can do it:
1. Start by picking a number and multiply it by each of the given numbers (1, 2, 6, and 8) one by one. For example, let's start with the number 10.
2. Multiply 10 by each of the given numbers:
- 10 * 1 = 10
- 10 * 2 = 20
- 10 * 6 = 60
- 10 * 8 = 80
3. Sum up the results: 10 + 20 + 60 + 80 = 170.
4. Compare the calculated sum (170) with the target number (1,428). Since 170 is much smaller than 1,428, we can conclude that the number we multiplied by (10) is too small.
5. Repeat the process with a larger number. Let's try using 100 this time.
6. Multiply 100 by each of the given numbers:
- 100 * 1 = 100
- 100 * 2 = 200
- 100 * 6 = 600
- 100 * 8 = 800
7. Calculate the sum: 100 + 200 + 600 + 800 = 1,700.
8. Since 1,700 is still smaller than 1,428, we can determine that the number we multiplied by (100) is too large.
9. Continue adjusting the number you multiply by, going smaller or larger depending on the results, until you find the approximate range in which the answer lies.
10. Once you've narrowed down the range to a smaller interval, you can use a more refined method (such as the bisection method or interpolation) to find the exact number.
Remember, this trial and error method can be a bit time-consuming but will eventually help you find the number you need to multiply by to get the desired result.