how many 3 digit numbers are divisible by 7

Three-digit numbers range from 100 to 999. To find how many three-digit numbers are divisible by 7, we identify the first and last three-digit multiples of 7.

First three-digit multiple of 7:
105 ÷ 7 = 15
So, 105 is the first three-digit number divisible by 7.

Last three-digit multiple of 7:
994 ÷ 7 = 142
So, 994 is the last three-digit number divisible by 7.

Now use the formula for counting terms in an arithmetic sequence:

Number of terms = [(Last − First) ÷ Common Difference] + 1

= [(994 − 105) ÷ 7] + 1
= 889 ÷ 7 + 1
= 127 + 1
= 128

Therefore, there are 128 three-digit numbers divisible by 7.

In conclusion, the total number of three-digit numbers divisible by 7 is 128.