Question

Using Euclid's division algorithm, find whether the pair of numbers 847, 2160 are coprimes or not.

Answer 1

Hi Friend,


a=2160,b=847
By Euclid's lemma,
a=bq+r,  0≤r<b                                   

2160=847×2+466
847=466×1+381
466=381×1+85
381=85×4+41
85=41×2+3
41=3×13+2
3=2×1+1
2=1×2+0
As 1 is the HCF of 847 and 216.  847 and 2160 are the co-primes.



Hope it helps you!! 

Answer 2

Answer :-

→ yes ✓ .

Step-by-step explanation :-

Firstly, we have to know what is co-prime numbers .

→ Those two numbers whose HCF is 1 , is known as co-prime numbers .

And , using Euclid's algorithm .

→ a = bq + r.

Q :- 847 , 2160 .

⇒ 2160 = 847 × 2 + 466 .

⇒ 847 = 466 × 1 + 381 .

⇒ 466 = 381 × 1 + 85 .

⇒ 381 = 85 × 4 + 41 .

⇒ 85 = 41 × 2 + 3 .

⇒ 41 = 3 × 13 + 2 .

⇒ 3 = 2 × 1 + 1 .

⇒ 2 = 1 × 2 + 0 .

∴ HCF( 847 , 2160 ) = 1 = 1 .

Hence, this pair is co-prime numbers .