Math, asked by ldrago4432, 1 year ago

Find the greatest number that will divide 445, 572 and 699 leaving reamainder 4, 5and 6 respectively by using euclids algorithm

Answers

Answered by dainvincible1
10
 445 - 4 = 441 
                 572 - 5 = 567 
                 699 - 6 = 693 
find the hcf 
441 = 3 x 3 x 7 x 7 
572 = 3 x 3 x 3 x 3 x 7 
693 = 3 x 3 x 7 x 11 
the common factors are 3 x 3 x 7 = 63 
HCF Of (441,567,693) = 63 
445 / 63 = 7 remainder 4 
572 / 63 = 9 remainder 5 
699 / 63 = 11 remainder 6 
63 is the answer

ldrago4432: Not by prime factorisation , by using euclids division algorithm
ldrago4432: Can you slove it using euclids division algorithm?
dainvincible1: i've done in Extended Euclidean algorithm
Answered by Fuschia
8
The numbers are --

445 - 4 = 441
572 - 5 = 567
699 - 6 = 693

The greatest and smallest number here are 693 and 441.

Apply the Euclid's algorithm,
693 = 441 × 1 + 252
441 = 252 × 1 + 189.
252 = 189 × 1 + 63
189 = 63 × 3 + 0
.
The divisor is the HCF of 693 and 441 that is 63.

Now let's check whether it completely divides 567
567 = 63 × 9 + 0

So , 63 is the greatest number that divides 445,572 and 699 by leaving reminders 4.,5 and 6 respectively

Hope This Helps You!
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