how many 2 digits numbers are there which are divisible by 6
15 I believe
smallest 12
largest 96
number of integers = (96-12)/6 + 1 = 15
To find the number of two-digit numbers that are divisible by 6, we can first determine the range of the two-digit numbers and then check which ones are divisible by 6.
The smallest two-digit number is 10, and the largest is 99. So, we need to find how many numbers in this range are divisible by 6.
To check if a number is divisible by 6, we need to check if it is divisible by both 2 and 3.
Firstly, let's check if the number is divisible by 2. For a number to be divisible by 2, its last digit must be an even number (0, 2, 4, 6, or 8). In this case, all the numbers between 10 and 99 satisfy this condition.
Next, we need to check if the number is divisible by 3. For a number to be divisible by 3, the sum of its digits must be divisible by 3.
The possible digit combinations for the tens and units digits are:
10, 11, 12, ..., 98, 99
To find out which combinations add up to a multiple of 3, we can look at the possible sums:
10 → 1 + 0 = 1 (not divisible by 3)
11 → 1 + 1 = 2 (not divisible by 3)
12 → 1 + 2 = 3 (divisible by 3)
...
98 → 9 + 8 = 17 (not divisible by 3)
99 → 9 + 9 = 18 (divisible by 3)
From the above analysis, we can see that the numbers with a tens digit summing to a multiple of 3 are:
12, 15, 18, ..., 96, 99
So, there are a total of nine two-digit numbers (12, 15, 18, ..., 96, 99) that are divisible by 6.