find the greatest number of 5 digit which when divided by 25 30 and 40 leaves a remainder of 20,25 and 35 respectively
Answers
Given:
The numbers = 25, 30 and 40
Remainder = 20, 25 and 35
To Find:
The greatest number of five digit
Solution:
Let the number dividing be = n
Thus, let the greater number be = n + 5
Now,
Taking the LCM of 25, 30 and 40 = 600.
As per question, we have to find the greatest number which when divided by 25, 35 and 40 leaves the remainder as 20, 25 and 35 respectively
Thus -
10000/600
= 166.6
Therefore, n = 5 = 166.6 x 600
= 99960
Number as per the question =
99960 - 5
= 99955.
Answer: The greatest number of five digit number is 99955.
99595 is the greatest number of 5 digit which when divided by 25 30 and 40 leaves a remainder of 20,25 and 35 respectively
Let say Number is N
N = 25A + 20 => N + 5 = 25(A + 1)
N = 30B + 25 => N + 5 = 30(B + 1)
N = 40C + 35 => N + 5 = 40(C + 1)
Hence N + 5 is the multiple of LCM of (25 , 30 , 40)
LCM - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.
LCM = product of each factor of highest power
25 = 5 x 5
30 = 2 x 3 x 5
40 = 2 x 2 x 2 x 5
LCM = 2 x 2 x 2 x 3 x 5 x 5 = 600
Hence N + 5 = 600k
600 x 166 = 99600
600 x 167 = 100200
As N is 5 digit number
Hence N + 5 = 99600 is possible
=> N = 99595
99595 is the greatest number of 5 digit which when divided by 25 30 and 40 leaves a remainder of 20,25 and 35 respectively
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