Use Euclid division lemma to justify that 1335 and 2034 are co_primes�

1.	Use Euclid division lemma to justify that 1335 and 2034 are co_primes
Answer» 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. $\:\:\:\:$ ________________________ Given: 1335 and 2034 are two co-prime numbers. To Find: Find by Euclid division lemma. $\:\:\:\:$ ________________________ 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. ____________________________

Use Euclid division lemma to justify that 1335 and 2034 are co_primes

Answer»

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.

$\:\:\:\:$ ________________________

Given:

1335 and 2034 are two co-prime numbers.

To Find:

Find by Euclid division lemma.

$\:\:\:\:$ ________________________

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.