Highest Common Factor of 7089, 6704 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 7089, 6704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7089, 6704 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 7089, 6704 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 7089, 6704 is 1.
HCF(7089, 6704) = 1
HCF of 7089, 6704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7089, 6704 is 1.
Highest Common Factor of 7089,6704 is 1
Step 1: Since 7089 > 6704, we apply the division lemma to 7089 and 6704, to get
7089 = 6704 x 1 + 385
Step 2: Since the reminder 6704 ≠ 0, we apply division lemma to 385 and 6704, to get
6704 = 385 x 17 + 159
Step 3: We consider the new divisor 385 and the new remainder 159, and apply the division lemma to get
385 = 159 x 2 + 67
We consider the new divisor 159 and the new remainder 67,and apply the division lemma to get
159 = 67 x 2 + 25
We consider the new divisor 67 and the new remainder 25,and apply the division lemma to get
67 = 25 x 2 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7089 and 6704 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(67,25) = HCF(159,67) = HCF(385,159) = HCF(6704,385) = HCF(7089,6704) .
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Frequently Asked Questions on HCF of 7089, 6704 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 7089, 6704?
Answer: HCF of 7089, 6704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7089, 6704 using Euclid's Algorithm?
Answer: For arbitrary numbers 7089, 6704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.