Highest Common Factor of 2206, 8356 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, 8356 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2206, 8356 is 2 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, 8356 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, 8356 is 2.
HCF(2206, 8356) = 2
HCF of 2206, 8356 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2206, 8356 is 2.
Highest Common Factor of 2206,8356 is 2
Step 1: Since 8356 > 2206, we apply the division lemma to 8356 and 2206, to get
8356 = 2206 x 3 + 1738
Step 2: Since the reminder 2206 ≠ 0, we apply division lemma to 1738 and 2206, to get
2206 = 1738 x 1 + 468
Step 3: We consider the new divisor 1738 and the new remainder 468, and apply the division lemma to get
1738 = 468 x 3 + 334
We consider the new divisor 468 and the new remainder 334,and apply the division lemma to get
468 = 334 x 1 + 134
We consider the new divisor 334 and the new remainder 134,and apply the division lemma to get
334 = 134 x 2 + 66
We consider the new divisor 134 and the new remainder 66,and apply the division lemma to get
134 = 66 x 2 + 2
We consider the new divisor 66 and the new remainder 2,and apply the division lemma to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2206 and 8356 is 2
Notice that 2 = HCF(66,2) = HCF(134,66) = HCF(334,134) = HCF(468,334) = HCF(1738,468) = HCF(2206,1738) = HCF(8356,2206) .
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Frequently Asked Questions on HCF of 2206, 8356 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, 8356?
Answer: HCF of 2206, 8356 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2206, 8356 using Euclid's Algorithm?
Answer: For arbitrary numbers 2206, 8356 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.