There are 75 three-digit numbers divisible by 12.
Understanding the Calculation
This can be calculated in a few ways. One method involves finding the smallest and largest three-digit numbers divisible by 12 and then determining the number of multiples within that range.
- Smallest: The smallest three-digit number is 100. Dividing 100 by 12 gives a quotient of 8 with a remainder of 4. Therefore, the smallest three-digit number divisible by 12 is 108 (12 x 9).
- Largest: The largest three-digit number is 999. Dividing 999 by 12 gives a quotient of 83 with a remainder of 3. Therefore, the largest three-digit number divisible by 12 is 996 (12 x 83).
- Number of Multiples: The numbers divisible by 12 form an arithmetic sequence with a common difference of 12. To find the number of terms in this sequence, we can use the formula: (Largest - Smallest) / Common Difference + 1. This gives us (996 - 108) / 12 + 1 = 75.
Examples of Three-Digit Numbers Divisible by 12
Here are a few examples to illustrate:
- 108
- 120
- 132
- ...
- 984
- 996
Several sources corroborate this answer, including various online forums and mathematical resources. For example, one Quora answer clearly states that there are 75 such numbers. Other sources confirm this result through similar calculations.
