Question

use Euclid division lemma to justify that 1335 and 2034 are co_primes​

Answer 1

According to the question:

• We are given with 1335 and 2034 these are two co- prime numbers which we have to justify to use of Euclid division lemma and we are said to find by Euclid division lemma.

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Given:

• 1335 and 2034 are two co-prime numbers.

To Find:

• Find by Euclid division lemma.

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Let consider a = 2034 and b = 1335 respectively.

$\: \: \sf \therefore \: by \: euclid \: divison \: lemma$

$\: \: \sf \: a = bq + r$

$\: \: \sf \: where \: 0 \leqslant r < b$

where....

• a = larger number
• b = smaller number
• q = Quotient
• r = Reminder

$\: \: \sf \: 2034 = 1335 \times 1 + 699 \\ \\ \: \: \sf \: 1335 = 699 \times 1 + 636 \\ \\ \: \: \sf \: 699 = 636 \times 1 + 63 \\ \\ \: \: \sf \: 636 = 63 \times 1 + 6 \\ \\ \: \: \sf \: 63 = 6 \times 1 + 3 \\ \\ \: \: \sf \: 6 = 3 \times 2 + 0$

Here,

we got remainder = 0

Hence,

3 is the HCF here and we are said that is it a co-prime and yes it is a co-prime number.

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