Question

By using the Euclid division algorithm find the HCF of 342 and 380?

Answer 1

Given:-

• 342 and 380  

To Find:-

• The HCF of 342 and 380 by using the Euclid division algorithm.

Solution:-

$\red{\sf{\longmapsto\:Euclid\:Division\:Lemma}}$

$\sf{\longmapsto\:a\:=\:bq\:+\:r}$

$\sf{\longmapsto\:0 \:≤\: r \:<\:b}$

Now,

Start with a larger integer, that is 380,

Applying Euclid's division lemma to 342 and 380, we get

a = bq + r

380 = 342 × 1 + 38

• Dividend = 342
• Divisor = 380
• qutiotiont = 1
• remainder = 38

Since the remainder 38 ≠ 0, we apply Euclid's division lemma to divisor 342 and remainder 0 to get

342 = 38 × 9 +  0

• Dividend = 38
• Divisor = 342
• qutiotiont = 9
• remainder = 0

We consider the new divisor 342 and remainder 0 and apply the division lemma.

Since the HCF of 342 and 380 is 38

Answer 2

Answer:

Given:-

342 and 380

To Find:-

The HCF of 342 and 380 by using the Euclid division algorithm.

Solution:-

⟼Euclid Division

⟼a=bq+r

⟼0 ≤ r < b

Now,

Start with a larger integer, that is 380,

Applying Euclid's division lemma to 342 and 380, we get

a = bq + r

380 = 342 × 1 + 38

Dividend = 342

Divisor = 380

qutiotiont = 1

remainder = 38

Since the remainder 38 ≠ 0, we apply Euclid's division lemma to divisor 342 and remainder 0 to get

342 = 38 × 9 + 0

Dividend = 38

Divisor = 342

qutiotiont = 9

remainder = 0

We consider the new divisor 342 and remainder 0 and apply the division lemma.

Since the HCF of 342 and 380 is 38

Step-by-step explanation:

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