Highest Common Factor of 838, 8704 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 838, 8704 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 838, 8704 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 838, 8704 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 838, 8704 is 2.
HCF(838, 8704) = 2
HCF of 838, 8704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 838, 8704 is 2.
Highest Common Factor of 838,8704 is 2
Step 1: Since 8704 > 838, we apply the division lemma to 8704 and 838, to get
8704 = 838 x 10 + 324
Step 2: Since the reminder 838 ≠ 0, we apply division lemma to 324 and 838, to get
838 = 324 x 2 + 190
Step 3: We consider the new divisor 324 and the new remainder 190, and apply the division lemma to get
324 = 190 x 1 + 134
We consider the new divisor 190 and the new remainder 134,and apply the division lemma to get
190 = 134 x 1 + 56
We consider the new divisor 134 and the new remainder 56,and apply the division lemma to get
134 = 56 x 2 + 22
We consider the new divisor 56 and the new remainder 22,and apply the division lemma to get
56 = 22 x 2 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 838 and 8704 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(56,22) = HCF(134,56) = HCF(190,134) = HCF(324,190) = HCF(838,324) = HCF(8704,838) .
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Frequently Asked Questions on HCF of 838, 8704 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 838, 8704?
Answer: HCF of 838, 8704 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 838, 8704 using Euclid's Algorithm?
Answer: For arbitrary numbers 838, 8704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.