Highest Common Factor of 308, 670, 129 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 308, 670, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 308, 670, 129 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 308, 670, 129 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 308, 670, 129 is 1.

HCF(308, 670, 129) = 1

HCF of 308, 670, 129 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 308, 670, 129 is 1.

Highest Common Factor of 308,670,129 using Euclid's algorithm

Highest Common Factor of 308,670,129 is 1

Step 1: Since 670 > 308, we apply the division lemma to 670 and 308, to get

670 = 308 x 2 + 54

Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 54 and 308, to get

308 = 54 x 5 + 38

Step 3: We consider the new divisor 54 and the new remainder 38, and apply the division lemma to get

54 = 38 x 1 + 16

We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get

38 = 16 x 2 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 308 and 670 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(54,38) = HCF(308,54) = HCF(670,308) .

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

Step 1: Since 129 > 2, we apply the division lemma to 129 and 2, to get

129 = 2 x 64 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 129 is 1

Notice that 1 = HCF(2,1) = HCF(129,2) .

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Frequently Asked Questions on HCF of 308, 670, 129 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 308, 670, 129?

Answer: HCF of 308, 670, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 308, 670, 129 using Euclid's Algorithm?

Answer: For arbitrary numbers 308, 670, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.