Highest Common Factor of 665, 421, 322 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 665, 421, 322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 421, 322 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 665, 421, 322 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 665, 421, 322 is 1.

HCF(665, 421, 322) = 1

HCF of 665, 421, 322 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 665, 421, 322 is 1.

Highest Common Factor of 665,421,322 using Euclid's algorithm

Highest Common Factor of 665,421,322 is 1

Step 1: Since 665 > 421, we apply the division lemma to 665 and 421, to get

665 = 421 x 1 + 244

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 244 and 421, to get

421 = 244 x 1 + 177

Step 3: We consider the new divisor 244 and the new remainder 177, and apply the division lemma to get

244 = 177 x 1 + 67

We consider the new divisor 177 and the new remainder 67,and apply the division lemma to get

177 = 67 x 2 + 43

We consider the new divisor 67 and the new remainder 43,and apply the division lemma to get

67 = 43 x 1 + 24

We consider the new divisor 43 and the new remainder 24,and apply the division lemma to get

43 = 24 x 1 + 19

We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get

24 = 19 x 1 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 421 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(43,24) = HCF(67,43) = HCF(177,67) = HCF(244,177) = HCF(421,244) = HCF(665,421) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 322 > 1, we apply the division lemma to 322 and 1, to get

322 = 1 x 322 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 322 is 1

Notice that 1 = HCF(322,1) .

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Frequently Asked Questions on HCF of 665, 421, 322 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 665, 421, 322?

Answer: HCF of 665, 421, 322 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 421, 322 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 421, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.