Highest Common Factor of 428, 691, 312 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 428, 691, 312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 428, 691, 312 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 428, 691, 312 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 428, 691, 312 is 1.

HCF(428, 691, 312) = 1

HCF of 428, 691, 312 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 428, 691, 312 is 1.

Highest Common Factor of 428,691,312 using Euclid's algorithm

Highest Common Factor of 428,691,312 is 1

Step 1: Since 691 > 428, we apply the division lemma to 691 and 428, to get

691 = 428 x 1 + 263

Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 263 and 428, to get

428 = 263 x 1 + 165

Step 3: We consider the new divisor 263 and the new remainder 165, and apply the division lemma to get

263 = 165 x 1 + 98

We consider the new divisor 165 and the new remainder 98,and apply the division lemma to get

165 = 98 x 1 + 67

We consider the new divisor 98 and the new remainder 67,and apply the division lemma to get

98 = 67 x 1 + 31

We consider the new divisor 67 and the new remainder 31,and apply the division lemma to get

67 = 31 x 2 + 5

We consider the new divisor 31 and the new remainder 5,and apply the division lemma to get

31 = 5 x 6 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 428 and 691 is 1

Notice that 1 = HCF(5,1) = HCF(31,5) = HCF(67,31) = HCF(98,67) = HCF(165,98) = HCF(263,165) = HCF(428,263) = HCF(691,428) .

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

Step 1: Since 312 > 1, we apply the division lemma to 312 and 1, to get

312 = 1 x 312 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 312 is 1

Notice that 1 = HCF(312,1) .

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Frequently Asked Questions on HCF of 428, 691, 312 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 428, 691, 312?

Answer: HCF of 428, 691, 312 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 428, 691, 312 using Euclid's Algorithm?

Answer: For arbitrary numbers 428, 691, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.