Question

Write Euclid's division algorithm​

Answer 1

a = bq + r

a and b are the dividend and the divisor.

q is the quotient.

r is the reminder

where ,

0 is greater or equal to r which is greater than b.

hope it helps you

please mark me as brainliest answer

Answer 2

Hello mate :)

Your answer is here:

Theorem : If a and b are ppositive integers such that a = bq + r, then every common divisor of a and b is a common divisor of b and r, and vice-versa.

Proof : Let c be a common divisor of a and b. Then,

c| a ⇒ a = cq1 for some integer q1

c| b ⇒ b = cq2 for some integer q2.

Now, a = bq + r

⇒ r = a – bq

⇒ r = cq1 – cq2 q

⇒ r = c( q1 – q2q)

⇒ c | r

⇒ c| r and c | b

⇒ c is a common divisor of b and r.

Hence, a common divisor of a and b is a common divisor of b and r.

Euclids Division Algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a and b.

$i hope it will help mate$