How many positive five-digit numbers are divisible by each of 7, 8, 9, 10, and 11?
+526 5-digit numbers divisible by 7 = 10003, 10010, 10017,..., 99995
So this is an AP with a = 10003, d = 7, and an = 99995
⇒ 99995 = 10003 + (n-1)7
⇒(n-1)7 = 89992
⇒ n = 12857
∴ 7 has 12857 5-digit factors.
Similarly,
5-digit numbers divisible by 8 = 10000, 10008, 10016,..., 99992
a = 10000, d = 8 and an = 99992
5-digit numbers divisible by 9 = 10008, 10017, 10026,..., 99999
a = 10008, d = 9 and an = 99999
5-digit numbers divisible by 10 = 10000, 10010, 10020,..., 99990
a = 10000, d = 10 and an = 99990
5-digit numbers divisible by 11 = 10010, 10021, 10032,..., 99990
a = 10010, d = 11 and an = 99990
...Rest you know how to find the total no. through AP...
~Hope you got it.
