What is the greatest number which divides 685 and 846 leaving remainder 5 and 6 respectively. pls answer with explanation.
Answers
Answer:
14280
Step-by-step explanation:
Subtract the remainders from the numbers.
=685-5; 846-6.
680;840.
Find the LCM of 680 and 840.
LCM of 680 and 840 is 14280.
Therefore answer is 14280.
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☆Answer ☆
Frist we have to subtract remainders from respective numbers.
685 - 5 = 680.
846 - 6 = 840.
Required number = HCF (840, 680)
HCF = 40 .
Hence, the HCF Is 40.
Note : I have find the HCF of it By long division method and Prime Factorization Method .
You Can see the Attachment.
☆Additional Information ☆
HCF - Highest common Factor.
LCM = Least common multiple .
We can use Euclid's division Algorithm to find the HCF of an given number
( This method is used in higher classes
Algorithm is a technique which we use to simplify our mathematical calculations .
The Euclid's division algorithm can also be refered as " Euclid's Division Lemma"
Euclid's division lemma states that for any positive integers a , b their an unique integers q , r . Satisfying the condition a = bq + r .
Similarly, their is a formula which relates LCM and HCF
That is ;
LCM x HCF = Product of 2 numbers
Example :-
LCM of 2 , 3 is 6
HCF of 2, 2 is 1
Using the formula ;
LCM x HCF = product of two numbers
6 x 1 = 2 x 3
6 = 6
Hence verified.
