Question

how many 4 digit numbers are multiples of 4 and 5​

Answer 1

uncountable number of 4 digit numbers are multiples of 4 and 5

Answer 2

There are 450 4-digit numbers that are multiples of 4 and 5 .

Explanation:

The least multiple of 4 and 5 = 4 x 5 = 20   ( ∵ 4 and 5 are co-primes).

The least 4-digit number divided by 20 = 1000

The greatest four digit number divided by 20 = 9980

In terms of A.P. the sequence of 4-digit numbers that area multiples of 20 will becomes :

1000 , 1020 , 1040 ,       ........ , 9980

Formula for nth term in A.P.  : $a_n=a+(n-1)d$ , where a= first term  , d common difference .

Put a= 1000 , d= 20 , $a_n=9980$ , we get

$9980= 1000+(n-1)20\\\\\Rightarrow\ 8980= 20(n-1)\\\\\Rightarrow\ n-1 =449\\\\\Rightarrow\ n=450$

Hence, there are 450 4-digit numbers that are multiples of 4 and 5​.

# Learn more :

How many 4 digit numbers are there with no digit repeated​

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