Question

Find the HCF of 816 and 170 using euclid's division algorithm and Express it in the form of 170x+816y where x and y are integers..​

Answer 1

Answer:

According to the fundamental theorem of arithmetic every composite number can be factorised as a product of primes and this factorization is unique apart from the order in which the prime factor occurs.

Fundamental theorem of arithmetic is also called unique factorization theorem.

Composite number = product of prime numbers.

Any Integer greater than 1, either be a prime number or can be written as a product of prime factors.

The prime factors of 816=2×2×2×2×3×17=2

4

×3×17

The prime factors of 170=2×5×17

LCM of 816 and 170=2

4

×3×5×17=4080

HCF of 816 and 170=2×17=34

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