The numbers from 1 to 100 that are not divisible by 5 are all numbers except those that end in 0 or 5. Figuring out what numbers ARE divisible by 5 is much easier, and then we can exclude those.
Here's how to approach finding the numbers not divisible by 5:
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Identify numbers divisible by 5: The multiples of 5 between 1 and 100 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, and 100. There are 20 such numbers (100 / 5 = 20).
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Exclude them from the total: Since there are 100 numbers in total, and 20 are divisible by 5, there are 100 - 20 = 80 numbers that are not divisible by 5.
Listing all 80 numbers is impractical. However, knowing how to identify them is key.
Instead of listing all 80 numbers, here's a breakdown:
- 1-4: All numbers (1, 2, 3, 4) are not divisible by 5.
- 6-9: All numbers (6, 7, 8, 9) are not divisible by 5.
- This pattern repeats for every ten numbers.
Therefore, 8 out of every 10 numbers are not divisible by 5.
The reference text mentions that 15, 30, 45, 60, 75, and 90 are multiples of 15, which are relevant if asking about divisibility by 15 (divisible by both 3 and 5).
