Highest Common Factor of 670, 771, 122 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 670, 771, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 670, 771, 122 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 670, 771, 122 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 670, 771, 122 is 1.

HCF(670, 771, 122) = 1

HCF of 670, 771, 122 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 670, 771, 122 is 1.

Highest Common Factor of 670,771,122 using Euclid's algorithm

Highest Common Factor of 670,771,122 is 1

Step 1: Since 771 > 670, we apply the division lemma to 771 and 670, to get

771 = 670 x 1 + 101

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 101 and 670, to get

670 = 101 x 6 + 64

Step 3: We consider the new divisor 101 and the new remainder 64, and apply the division lemma to get

101 = 64 x 1 + 37

We consider the new divisor 64 and the new remainder 37,and apply the division lemma to get

64 = 37 x 1 + 27

We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get

37 = 27 x 1 + 10

We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get

27 = 10 x 2 + 7

We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get

10 = 7 x 1 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 670 and 771 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(64,37) = HCF(101,64) = HCF(670,101) = HCF(771,670) .

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

Step 1: Since 122 > 1, we apply the division lemma to 122 and 1, to get

122 = 1 x 122 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1

Notice that 1 = HCF(122,1) .

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Frequently Asked Questions on HCF of 670, 771, 122 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 670, 771, 122?

Answer: HCF of 670, 771, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 670, 771, 122 using Euclid's Algorithm?

Answer: For arbitrary numbers 670, 771, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.