How many three digit number are divisible by both 2 and 5
Answers
A.P. 110,120,130,.....,990
a = 110 , d = 120-110 = 10
an = a+(n-1)d
990 = 110 +(n-1)10
880/10 = n-1
n = 88+1
n = 89
so answer there are 89 numbers which are divisible by both 2&5
The Total Number Of 3-digit Numbers Divisible By 2 And 5 Is 90.
GIVEN
Numbers 2 and 5.
TO FIND
Total number of 3-digit numbers divisible by the given numbers.
SOLUTION
We can simply solve the above problem as follows-
A number that will be divisible by both 2 and 5 will also be divisible by, 5×2 = 10.
Lowest 3-digit number = 100
The greatest three-digit number = is 999
Lowest 3- digit number exactly divisible by 10 = 100
Greatest 3-digit number is exactly divisible by 10 = 990.
This is an arithmetic progression, represented by the formula -
l = a + (n-1)d
Where,
l = last term in the sequence
a= first term in the sequence (100 in this case)
n = number of terms
d = common difference.
990 = 100+(n-1)10
990 = 100 + 10n - 10
990 = 90 + 10n
990-90 = 10n
900 = 10n
n = 900/10 = 90
Hence, the Total number of 3-digit numbers divisible by 2 and 5 is 90.
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