What are the multiples of 3 up to 100?
The Correct Answer and Explanation is :
The multiples of 3 up to 100 are:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
To understand why these numbers are multiples of 3, it’s essential to recognize that a multiple of a number is the product of that number and an integer. In this case, the number is 3. Therefore, we can find the multiples of 3 by multiplying 3 by the integers from 1 to 33 (since (3 \times 33 = 99) is the largest multiple of 3 below 100).
Here’s a breakdown of how the multiplication works:
- First Multiple: (3 \times 1 = 3)
- Second Multiple: (3 \times 2 = 6)
- Third Multiple: (3 \times 3 = 9)
- …
- Final Multiple Below 100: (3 \times 33 = 99)
The pattern here is clear: each successive multiple increases by 3. This sequence can also be visualized as an arithmetic progression where the first term is 3 and the common difference is also 3.
Furthermore, identifying multiples of a number like 3 has practical applications, such as in divisibility rules. A number is divisible by 3 if the sum of its digits is divisible by 3. For example, in the number 27, (2 + 7 = 9), and since 9 is divisible by 3, so is 27.
In summary, the multiples of 3 up to 100 are formed by taking the integer multiples of 3, and they exhibit consistent patterns that are useful in various mathematical and real-world applications.