Highest Common Factor of 820, 309 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 820, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 309 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 820, 309 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 820, 309 is 1.
HCF(820, 309) = 1
HCF of 820, 309 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 309 is 1.
Highest Common Factor of 820,309 is 1
Step 1: Since 820 > 309, we apply the division lemma to 820 and 309, to get
820 = 309 x 2 + 202
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 202 and 309, to get
309 = 202 x 1 + 107
Step 3: We consider the new divisor 202 and the new remainder 107, and apply the division lemma to get
202 = 107 x 1 + 95
We consider the new divisor 107 and the new remainder 95,and apply the division lemma to get
107 = 95 x 1 + 12
We consider the new divisor 95 and the new remainder 12,and apply the division lemma to get
95 = 12 x 7 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 820 and 309 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(95,12) = HCF(107,95) = HCF(202,107) = HCF(309,202) = HCF(820,309) .
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Frequently Asked Questions on HCF of 820, 309 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 820, 309?
Answer: HCF of 820, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.