find number of three digit numbers divisible by 45 and whose digits are in a.p
Answers
Answer:
765 is a no. which divisible by 45 and 5,6,7 are in a. p.
Answer:
The three digit numbers can be 102,111,120…999.
Step-by-step explanation:
If a number can be divided by both 9 and 5, it can also be divided by 45. A number is divisible by 9 if its digit sum is divisible by 9, and by 5 if its units digit is either 0 or 5.
A three-digit integer must have a units digit of either 0 or 5 and its digits must form an arithmetic progression (A.P) with a common difference of 9 in order to be divisible by 45. The first and last three-digit numbers in A.P. with a common difference of 9 are 102 and 993, respectively.
Therefore, the possible three-digit numbers that are divisible by 45 and whose digits are in an A.P are 102, 111, 120, ..., 990, 999. There are a total of (999 - 102) / 9 + 1 = 100 such numbers.
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