What are the values of M and N respectively if 1M39048458N is divisible by both 8 and 9, where M and N are single-digit integers?
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Answer:
M=8
N=4
18390484584 is the required number.
Step-by-step explanation:
For any number to be divisible by 9, divisibility rule states that the sum of all the digits should either be 9 or a multiple of 9.
hence, 1+M+3+9+0+4+8+4+5+8+N=9c( where c is some random number, which is taken just for convenience, and really does not mean anything because sum of digits for any multiple of 9 is also 9 )
equation M+N+42=9c
also, as per divisibility rule for 8, last 3 digits should be divisible by 8.
hence, 58N should be divisible by 8
so, N =4, since only 584 is exactly divisible by 8.
now, coming to earlier equation,
M+N+42=9c
M+46=9c
M+46=54
M=8
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