How Many Two-Digit Numbers Are Divisible by 7?

There are 13 two-digit numbers divisible by 7.

This can be determined by identifying the first and last two-digit numbers divisible by 7, and then calculating the number of terms in the resulting arithmetic sequence.

• The first two-digit number divisible by 7 is 14 (7 x 2).
• The last two-digit number divisible by 7 is 98 (7 x 14).
• The common difference between consecutive two-digit multiples of 7 is 7.

We can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.

In this case:

• a_n = 98
• a_1 = 14
• d = 7

Solving for n:

98 = 14 + (n - 1)7

84 = (n - 1)7

12 = n - 1

n = 13

Therefore, there are 13 two-digit numbers divisible by 7. This is confirmed across multiple sources, including those provided as references which list the sequence as 14, 21, 28, 35...98.