Find the greatest number that will divide 445, 572 and 699 leaving reamainder 4, 5and 6 respectively by using euclids algorithm
Answers
Answered by
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
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
Can you slove it using euclids division algorithm?
i've done in Extended Euclidean algorithm
Answered by
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!
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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