Let's solve the given question:

"How many numbers are divisible by 8 from 101–200?"

Solution:

To determine how many numbers between 101 and 200 are divisible by 8, we follow these steps:

1. Find the first number divisible by 8 in this range:

   • Start from 101 and check for divisibility by 8.
   • $104$ is the first number divisible by 8 because: $104 \div 8 = 13 \, \text{(exactly divisible)}.$

2. Find the last number divisible by 8 in this range:

   • Start from 200 and check for divisibility by 8.
   • $200$ is the last number divisible by 8 because: $200 \div 8 = 25 \, \text{(exactly divisible)}.$

3. Count all multiples of 8 between 104 and 200:

   • The multiples of 8 form an arithmetic sequence: $104, 112, 120, \dots, 200$

     • First term ($a$) = 104
     • Last term ($l$) = 200
     • Common difference ($d$) = 8

   • Use the formula for the $n$-th term of an arithmetic sequence: $l = a + (n - 1) \cdot d$ Substituting values: $200 = 104 + (n - 1) \cdot 8$ $200 - 104 = (n - 1) \cdot 8$ $96 = (n - 1) \cdot 8$ $n - 1 = 12 \quad \Rightarrow \quad n = 13$

Final Answer:

There are 13 numbers divisible by 8 between 101 and 200.

Correct Option:

B. 13

Would you like a further explanation, or do you have other questions? 😊

Related Questions:

1. What is the sum of all numbers divisible by 8 between 101 and 200?
2. How many numbers between 101 and 200 are divisible by both 8 and 4?
3. What is the greatest common divisor (GCD) of the numbers divisible by 8 in this range?
4. How many odd numbers are there between 101 and 200?
5. How many numbers between 101 and 200 are divisible by 3?

Tip:

When solving problems with multiples, always use the formula for an arithmetic sequence to find the total number of terms quickly.