Highest Common Factor of 431, 656, 705 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 431, 656, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 431, 656, 705 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 431, 656, 705 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 431, 656, 705 is 1.

HCF(431, 656, 705) = 1

HCF of 431, 656, 705 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 431, 656, 705 is 1.

Highest Common Factor of 431,656,705 using Euclid's algorithm

Highest Common Factor of 431,656,705 is 1

Step 1: Since 656 > 431, we apply the division lemma to 656 and 431, to get

656 = 431 x 1 + 225

Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 225 and 431, to get

431 = 225 x 1 + 206

Step 3: We consider the new divisor 225 and the new remainder 206, and apply the division lemma to get

225 = 206 x 1 + 19

We consider the new divisor 206 and the new remainder 19,and apply the division lemma to get

206 = 19 x 10 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 431 and 656 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(206,19) = HCF(225,206) = HCF(431,225) = HCF(656,431) .

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

Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get

705 = 1 x 705 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1

Notice that 1 = HCF(705,1) .

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Frequently Asked Questions on HCF of 431, 656, 705 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 431, 656, 705?

Answer: HCF of 431, 656, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 431, 656, 705 using Euclid's Algorithm?

Answer: For arbitrary numbers 431, 656, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.