Highest Common Factor of 306, 878, 613, 358 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 306, 878, 613, 358 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 306, 878, 613, 358 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 306, 878, 613, 358 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 306, 878, 613, 358 is 1.

HCF(306, 878, 613, 358) = 1

HCF of 306, 878, 613, 358 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 306, 878, 613, 358 is 1.

Highest Common Factor of 306,878,613,358 using Euclid's algorithm

Highest Common Factor of 306,878,613,358 is 1

Step 1: Since 878 > 306, we apply the division lemma to 878 and 306, to get

878 = 306 x 2 + 266

Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 266 and 306, to get

306 = 266 x 1 + 40

Step 3: We consider the new divisor 266 and the new remainder 40, and apply the division lemma to get

266 = 40 x 6 + 26

We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get

40 = 26 x 1 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 306 and 878 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(266,40) = HCF(306,266) = HCF(878,306) .

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

Step 1: Since 613 > 2, we apply the division lemma to 613 and 2, to get

613 = 2 x 306 + 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 613 is 1

Notice that 1 = HCF(2,1) = HCF(613,2) .

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

Step 1: Since 358 > 1, we apply the division lemma to 358 and 1, to get

358 = 1 x 358 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 358 is 1

Notice that 1 = HCF(358,1) .

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Frequently Asked Questions on HCF of 306, 878, 613, 358 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 306, 878, 613, 358?

Answer: HCF of 306, 878, 613, 358 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 306, 878, 613, 358 using Euclid's Algorithm?

Answer: For arbitrary numbers 306, 878, 613, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.