Highest Common Factor of 8215, 3409, 67674 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 8215, 3409, 67674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8215, 3409, 67674 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 8215, 3409, 67674 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 8215, 3409, 67674 is 1.

HCF(8215, 3409, 67674) = 1

HCF of 8215, 3409, 67674 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 8215, 3409, 67674 is 1.

Highest Common Factor of 8215,3409,67674 using Euclid's algorithm

Highest Common Factor of 8215,3409,67674 is 1

Step 1: Since 8215 > 3409, we apply the division lemma to 8215 and 3409, to get

8215 = 3409 x 2 + 1397

Step 2: Since the reminder 3409 ≠ 0, we apply division lemma to 1397 and 3409, to get

3409 = 1397 x 2 + 615

Step 3: We consider the new divisor 1397 and the new remainder 615, and apply the division lemma to get

1397 = 615 x 2 + 167

We consider the new divisor 615 and the new remainder 167,and apply the division lemma to get

615 = 167 x 3 + 114

We consider the new divisor 167 and the new remainder 114,and apply the division lemma to get

167 = 114 x 1 + 53

We consider the new divisor 114 and the new remainder 53,and apply the division lemma to get

114 = 53 x 2 + 8

We consider the new divisor 53 and the new remainder 8,and apply the division lemma to get

53 = 8 x 6 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 8215 and 3409 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(53,8) = HCF(114,53) = HCF(167,114) = HCF(615,167) = HCF(1397,615) = HCF(3409,1397) = HCF(8215,3409) .

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

Step 1: Since 67674 > 1, we apply the division lemma to 67674 and 1, to get

67674 = 1 x 67674 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67674 is 1

Notice that 1 = HCF(67674,1) .

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Frequently Asked Questions on HCF of 8215, 3409, 67674 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 8215, 3409, 67674?

Answer: HCF of 8215, 3409, 67674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8215, 3409, 67674 using Euclid's Algorithm?

Answer: For arbitrary numbers 8215, 3409, 67674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.