using Euclid's algorithm find which of the following pairs of numbers are co-primes ;
1) 231,396
2) 847,2160
Answers
Answer :-
→ 1 not , 2 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.
Now,
Q :- 1) 231 , 396 .
⇒ 396 = 231 × 1 + 165 .
⇒ 231 = 165 × 1 + 66 .
⇒ 165 = 66 × 2 + 33.
⇒ 66 = 33 × 2 + 0 .
∴ HCf ( 231 , 396 ) = 33 ≠ 1 .
Hence, this pair is not co-prime numbers .
Q :- 2) 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 .
Q. no :- 1) 231 , 396 .
⇒ 396 = 231 × 1 + 165 .
⇒ 231 = 165 × 1 + 66 .
⇒ 165 = 66 × 2 + 33.
⇒ 66 = 33 × 2 + 0 .
∴ HCf ( 231 , 396 ) = 33 .
this pair is not co-prime numbers .
Q. no :- 2) 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
this pair is co-prime numbers .