48.
The first two digit number is 10, the last two digit number is 99, so there are 99 - 10 + 1 = 90 two digit numbers
→ 10 ÷ 3 = 31/3 → first two digit number divisible by 3 is 4 x 3 = 12
→ 99 ÷ 3 = 33 → last two digit number divisible by 3 is 33 x 3 = 99
→ 33 - 4 + 1 = 30 two digit numbers divisible by 3
→ 10 ÷ 5 = 2 → first two digit number divisible by 5 is 2 x 5 = 10
→ 99 ÷ 5 = 194/5 → last two digit number divisible by 5 is 19 x 5 = 95
→ 19 - 2 + 1 = 18 two digit numbers divisible by 5
→ 30 + 18 = 48 two digit numbers divisible by 3 or 5 OR BOTH.
The numbers divisible by both are multiples of their lowest common multiple: lcm(3, 5) = 15, and have been counted twice, so need to be subtracted from the total
→ 10 ÷ 15 = 010/15 → first two digit number divisible by 15 is 1 x 15 = 15
→ 99 ÷ 15 = 69/15 → last two digit number divisible by 15 is 6 x 15 = 90
→ 6 - 1 + 1 = 6 two digit numbers divisible by 15 (the lcm of 3 and 5)
→ 48 - 6 = 42 two digit numbers divisible by 3 or 5.
→ 90 - 42 = 48 two digit numbers divisible by neither 3 nor 5.
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There are 151 3-digit numbers that are divisible by 6.
There are 180 3-digit numbers divisible by five.
Starting at 12 and ending at 99, there are 30 two-digit numbers divisible by three.
How many two digit number are divisible by 5
Oh, isn't that a happy little question! To find the two-digit numbers divisible by 3, we start by finding the first two-digit number divisible by 3, which is 12. Then, we find the last two-digit number divisible by 3, which is 99. Now, we can count how many numbers there are between 12 and 99 that are divisible by 3.