Highest Common Factor of 2206, 3423, 85698 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 2206, 3423, 85698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2206, 3423, 85698 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 2206, 3423, 85698 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 2206, 3423, 85698 is 1.

HCF(2206, 3423, 85698) = 1

HCF of 2206, 3423, 85698 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 2206, 3423, 85698 is 1.

Highest Common Factor of 2206,3423,85698 using Euclid's algorithm

Highest Common Factor of 2206,3423,85698 is 1

Step 1: Since 3423 > 2206, we apply the division lemma to 3423 and 2206, to get

3423 = 2206 x 1 + 1217

Step 2: Since the reminder 2206 ≠ 0, we apply division lemma to 1217 and 2206, to get

2206 = 1217 x 1 + 989

Step 3: We consider the new divisor 1217 and the new remainder 989, and apply the division lemma to get

1217 = 989 x 1 + 228

We consider the new divisor 989 and the new remainder 228,and apply the division lemma to get

989 = 228 x 4 + 77

We consider the new divisor 228 and the new remainder 77,and apply the division lemma to get

228 = 77 x 2 + 74

We consider the new divisor 77 and the new remainder 74,and apply the division lemma to get

77 = 74 x 1 + 3

We consider the new divisor 74 and the new remainder 3,and apply the division lemma to get

74 = 3 x 24 + 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 2206 and 3423 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(74,3) = HCF(77,74) = HCF(228,77) = HCF(989,228) = HCF(1217,989) = HCF(2206,1217) = HCF(3423,2206) .

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

Step 1: Since 85698 > 1, we apply the division lemma to 85698 and 1, to get

85698 = 1 x 85698 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 85698 is 1

Notice that 1 = HCF(85698,1) .

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Frequently Asked Questions on HCF of 2206, 3423, 85698 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 2206, 3423, 85698?

Answer: HCF of 2206, 3423, 85698 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2206, 3423, 85698 using Euclid's Algorithm?

Answer: For arbitrary numbers 2206, 3423, 85698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.