To find how many multiples of 4 lie between 10 and 250, we need to identify the first and last multiples of 4 within this range.
1. **Finding the first multiple of 4 greater than or equal to 10:**
The first multiple of 4 that is greater than or equal to 10 can be calculated by rounding up 10 to the nearest multiple of 4. Since 10 divided by 4 is 2.5, we round it up to 3 and then multiply by 4:
3 x 4 = 12
So, the first multiple of 4 in our range is 12.
2. **Finding the last multiple of 4 less than or equal to 250:**
The last multiple of 4 that is less than or equal to 250 can be calculated by rounding down 250 to the nearest multiple of 4. Since 250 divided by 4 is 62.5, we round it down to 62 and then multiply by 4:
62 x 4 = 248
So, the last multiple of 4 in our range is 248.
3. **Counting the multiples of 4 from 12 to 248:**
The multiples of 4 can be expressed as:
4n where n is any integer.
For our range, we can set up the equation:
4n = 12 to 248
To find n, we divide each part of the range by 4:
n = 3 to 62
We can now find how many integers lie between 3 and 62, inclusive. To do this, we simply subtract:
62 – 3 + 1 = 60
This means there are 60 multiples of 4 between 10 and 250.
In conclusion, the multiples of 4 that lie between 10 and 250 are plentiful, and we determined that there are 60 such multiples in this range.