how many numbers between 100 and 500 are divisible bye 2 , 3 and 7 together?
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For a number to be divisible by 2,3,7 together, it should be L.C.M of 2,3,7
L.C.M of (2,3,7) = 42
To find the number of numbers between 100 and 500 divisible by (2,3,7) or 42:
100/42 = Quotient 2
500/42 = Quotient 11
Hence number of numbers= 11-2 = 9
Or
126 is the first number after 100 that is divisible by '42' [100/42==Remainder = 16..hence 'add 26 to 100' to get a num divisible by 42 > 100]
462 is the last number less than 500 that is divisible by '42' [500/42 = Remainder 38. Hence subtarct 38 from 500 to get the last number less than 500 which is divisible by 42]
Now, its an A.P
126, 168......462
A1 = 126
An = 462
d = 42
An = A1 + (n-1)*d
462 = 126 + (n-1)*42
336 = (n-1) * 42
n-1 = 8
n = 9
Hence '9' numbers are there b/w 100 and 500 which is exactly divisible by 2,3,7 together.
Hope it helps.
L.C.M of (2,3,7) = 42
To find the number of numbers between 100 and 500 divisible by (2,3,7) or 42:
100/42 = Quotient 2
500/42 = Quotient 11
Hence number of numbers= 11-2 = 9
Or
126 is the first number after 100 that is divisible by '42' [100/42==Remainder = 16..hence 'add 26 to 100' to get a num divisible by 42 > 100]
462 is the last number less than 500 that is divisible by '42' [500/42 = Remainder 38. Hence subtarct 38 from 500 to get the last number less than 500 which is divisible by 42]
Now, its an A.P
126, 168......462
A1 = 126
An = 462
d = 42
An = A1 + (n-1)*d
462 = 126 + (n-1)*42
336 = (n-1) * 42
n-1 = 8
n = 9
Hence '9' numbers are there b/w 100 and 500 which is exactly divisible by 2,3,7 together.
Hope it helps.
Answered by
0
Answer:
2744756
Step-by-step explanation:
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