Highest Common Factor of 322, 443, 705 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 322, 443, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 322, 443, 705 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 322, 443, 705 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 322, 443, 705 is 1.

HCF(322, 443, 705) = 1

HCF of 322, 443, 705 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 322, 443, 705 is 1.

Highest Common Factor of 322,443,705 using Euclid's algorithm

Highest Common Factor of 322,443,705 is 1

Step 1: Since 443 > 322, we apply the division lemma to 443 and 322, to get

443 = 322 x 1 + 121

Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 121 and 322, to get

322 = 121 x 2 + 80

Step 3: We consider the new divisor 121 and the new remainder 80, and apply the division lemma to get

121 = 80 x 1 + 41

We consider the new divisor 80 and the new remainder 41,and apply the division lemma to get

80 = 41 x 1 + 39

We consider the new divisor 41 and the new remainder 39,and apply the division lemma to get

41 = 39 x 1 + 2

We consider the new divisor 39 and the new remainder 2,and apply the division lemma to get

39 = 2 x 19 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 322 and 443 is 1

Notice that 1 = HCF(2,1) = HCF(39,2) = HCF(41,39) = HCF(80,41) = HCF(121,80) = HCF(322,121) = HCF(443,322) .

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

Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get

705 = 1 x 705 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1

Notice that 1 = HCF(705,1) .

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Frequently Asked Questions on HCF of 322, 443, 705 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 322, 443, 705?

Answer: HCF of 322, 443, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 322, 443, 705 using Euclid's Algorithm?

Answer: For arbitrary numbers 322, 443, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.