find the greatest number of 4 digit when divided by 7 10 15 21 and 28 leaves the remainders 5 8 13 19 26 respectively
Answers
Concept:
In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
We have two key techniques—the division method and the prime factorization approach—for determining H.C.F. and L.C.M.
Given:
The greatest number of 4 digit when divided by 7 10 15 21 and 28 leaves the remainders 5 8 13 19 26 respectively
Find:
Find the number
Solution:
You can see the difference between divisor and remainder is 2
7-5=10-8=15-13=21-19=28-26=2
largest 4 digit number=9999
LCM of 7,10,15,21,28=420
9999=420×23+339
9999-339=9660
Means 9660 is largest 4 digit no that is completely divisible by given numbers .
But after subtracting 2 we get the required n.
9660-2=9658
Therefore the greatest number of 4 digit when divided by 7 10 15 21 and 28 leaves the remainders 5 8 13 19 26 respectively is 9658
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Step-by-step explanation:
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