Highest Common Factor of 310, 473, 822 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 310, 473, 822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 473, 822 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 310, 473, 822 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 310, 473, 822 is 1.

HCF(310, 473, 822) = 1

HCF of 310, 473, 822 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 310, 473, 822 is 1.

Highest Common Factor of 310,473,822 using Euclid's algorithm

Highest Common Factor of 310,473,822 is 1

Step 1: Since 473 > 310, we apply the division lemma to 473 and 310, to get

473 = 310 x 1 + 163

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 163 and 310, to get

310 = 163 x 1 + 147

Step 3: We consider the new divisor 163 and the new remainder 147, and apply the division lemma to get

163 = 147 x 1 + 16

We consider the new divisor 147 and the new remainder 16,and apply the division lemma to get

147 = 16 x 9 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 310 and 473 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(147,16) = HCF(163,147) = HCF(310,163) = HCF(473,310) .

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

Step 1: Since 822 > 1, we apply the division lemma to 822 and 1, to get

822 = 1 x 822 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 822 is 1

Notice that 1 = HCF(822,1) .

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Frequently Asked Questions on HCF of 310, 473, 822 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 310, 473, 822?

Answer: HCF of 310, 473, 822 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 473, 822 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 473, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.