Highest Common Factor of 667, 912, 776 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, 912, 776 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 667, 912, 776 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, 912, 776 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, 912, 776 is 1.

HCF(667, 912, 776) = 1

HCF of 667, 912, 776 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, 912, 776 is 1.

Highest Common Factor of 667,912,776 using Euclid's algorithm

Highest Common Factor of 667,912,776 is 1

Step 1: Since 912 > 667, we apply the division lemma to 912 and 667, to get

912 = 667 x 1 + 245

Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 245 and 667, to get

667 = 245 x 2 + 177

Step 3: We consider the new divisor 245 and the new remainder 177, and apply the division lemma to get

245 = 177 x 1 + 68

We consider the new divisor 177 and the new remainder 68,and apply the division lemma to get

177 = 68 x 2 + 41

We consider the new divisor 68 and the new remainder 41,and apply the division lemma to get

68 = 41 x 1 + 27

We consider the new divisor 41 and the new remainder 27,and apply the division lemma to get

41 = 27 x 1 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 912 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(68,41) = HCF(177,68) = HCF(245,177) = HCF(667,245) = HCF(912,667) .

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

Step 1: Since 776 > 1, we apply the division lemma to 776 and 1, to get

776 = 1 x 776 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 776 is 1

Notice that 1 = HCF(776,1) .

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Frequently Asked Questions on HCF of 667, 912, 776 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, 912, 776?

Answer: HCF of 667, 912, 776 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 667, 912, 776 using Euclid's Algorithm?

Answer: For arbitrary numbers 667, 912, 776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.