Highest Common Factor of 914, 586, 232, 675 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 914, 586, 232, 675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 914, 586, 232, 675 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 914, 586, 232, 675 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 914, 586, 232, 675 is 1.

HCF(914, 586, 232, 675) = 1

HCF of 914, 586, 232, 675 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 914, 586, 232, 675 is 1.

Highest Common Factor of 914,586,232,675 using Euclid's algorithm

Highest Common Factor of 914,586,232,675 is 1

Step 1: Since 914 > 586, we apply the division lemma to 914 and 586, to get

914 = 586 x 1 + 328

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 328 and 586, to get

586 = 328 x 1 + 258

Step 3: We consider the new divisor 328 and the new remainder 258, and apply the division lemma to get

328 = 258 x 1 + 70

We consider the new divisor 258 and the new remainder 70,and apply the division lemma to get

258 = 70 x 3 + 48

We consider the new divisor 70 and the new remainder 48,and apply the division lemma to get

70 = 48 x 1 + 22

We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get

48 = 22 x 2 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 914 and 586 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(70,48) = HCF(258,70) = HCF(328,258) = HCF(586,328) = HCF(914,586) .

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

Step 1: Since 232 > 2, we apply the division lemma to 232 and 2, to get

232 = 2 x 116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 232 is 2

Notice that 2 = HCF(232,2) .

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

Step 1: Since 675 > 2, we apply the division lemma to 675 and 2, to get

675 = 2 x 337 + 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 675 is 1

Notice that 1 = HCF(2,1) = HCF(675,2) .

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Frequently Asked Questions on HCF of 914, 586, 232, 675 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 914, 586, 232, 675?

Answer: HCF of 914, 586, 232, 675 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 914, 586, 232, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 914, 586, 232, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.