Highest Common Factor of 9806, 2122 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 9806, 2122 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9806, 2122 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 9806, 2122 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 9806, 2122 is 2.
HCF(9806, 2122) = 2
HCF of 9806, 2122 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9806, 2122 is 2.
Highest Common Factor of 9806,2122 is 2
Step 1: Since 9806 > 2122, we apply the division lemma to 9806 and 2122, to get
9806 = 2122 x 4 + 1318
Step 2: Since the reminder 2122 ≠ 0, we apply division lemma to 1318 and 2122, to get
2122 = 1318 x 1 + 804
Step 3: We consider the new divisor 1318 and the new remainder 804, and apply the division lemma to get
1318 = 804 x 1 + 514
We consider the new divisor 804 and the new remainder 514,and apply the division lemma to get
804 = 514 x 1 + 290
We consider the new divisor 514 and the new remainder 290,and apply the division lemma to get
514 = 290 x 1 + 224
We consider the new divisor 290 and the new remainder 224,and apply the division lemma to get
290 = 224 x 1 + 66
We consider the new divisor 224 and the new remainder 66,and apply the division lemma to get
224 = 66 x 3 + 26
We consider the new divisor 66 and the new remainder 26,and apply the division lemma to get
66 = 26 x 2 + 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 9806 and 2122 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(66,26) = HCF(224,66) = HCF(290,224) = HCF(514,290) = HCF(804,514) = HCF(1318,804) = HCF(2122,1318) = HCF(9806,2122) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9806, 2122 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 9806, 2122?
Answer: HCF of 9806, 2122 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9806, 2122 using Euclid's Algorithm?
Answer: For arbitrary numbers 9806, 2122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
