Question 1029343: How many 3-digit numbers are multiple of 21?
I can solve it by counting there is another way to solve this type of problem
Thanks
Found 3 solutions by robertb, ikleyn, Edwin McCravy:
Answer by robertb(5830)   (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
How many 3-digit numbers are multiple of 21?
I can solve it by counting there is another way to solve this type of problem
Thanks
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First such number is 105.
Last such number is 987.
How many intervals by 21 integer numbers are between these two numbers?
It is
 = 42.
So, there are 42 intervals.
Hence, the number of multiples 21 from 105 to 987 inclusively is 42 + 1 = 43.
Answer. There are 43 multiples of 21 that are 3-digit integers.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
The smallest 3-digit number is 100 and the largest
3-digit number is 999.
Dividing 100 by 21 gives 4.76, which rounds up to 5,
so the smallest 3-digit multiple of 21 will be 5*21 or 105.
Dividing 999 by 21 gives 47.57, which rounds down to
47, so the largest 3-digit multiple of 21 will be 47*21 or 987.
So the 3-digit multiples of 21 form the arithmetic sequence
5*21,6*21,...,46*21,47*21
Dividing them all by 21 gives the sequence
5,6,...,46,47, which has the same number of terms.
Subtracting 4 from each gives the sequence
1,2...,42,43, which also has the same number of terms.
Answer: 43
Edwin
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