Highest Common Factor of 667, 903, 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 667, 903, 322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 667, 903, 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 667, 903, 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 667, 903, 322 is 1.

HCF(667, 903, 322) = 1

HCF of 667, 903, 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 667, 903, 322 is 1.

Highest Common Factor of 667,903,322 using Euclid's algorithm

Highest Common Factor of 667,903,322 is 1

Step 1: Since 903 > 667, we apply the division lemma to 903 and 667, to get

903 = 667 x 1 + 236

Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 236 and 667, to get

667 = 236 x 2 + 195

Step 3: We consider the new divisor 236 and the new remainder 195, and apply the division lemma to get

236 = 195 x 1 + 41

We consider the new divisor 195 and the new remainder 41,and apply the division lemma to get

195 = 41 x 4 + 31

We consider the new divisor 41 and the new remainder 31,and apply the division lemma to get

41 = 31 x 1 + 10

We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get

31 = 10 x 3 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 903 is 1

Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(41,31) = HCF(195,41) = HCF(236,195) = HCF(667,236) = HCF(903,667) .

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 667, 903, 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 667, 903, 322?

Answer: HCF of 667, 903, 322 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 667, 903, 322 using Euclid's Algorithm?

Answer: For arbitrary numbers 667, 903, 322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.