Highest Common Factor of 767, 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 767, 6704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 767, 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 767, 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 767, 6704 is 1.
HCF(767, 6704) = 1
HCF of 767, 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 767, 6704 is 1.
Highest Common Factor of 767,6704 is 1
Step 1: Since 6704 > 767, we apply the division lemma to 6704 and 767, to get
6704 = 767 x 8 + 568
Step 2: Since the reminder 767 ≠ 0, we apply division lemma to 568 and 767, to get
767 = 568 x 1 + 199
Step 3: We consider the new divisor 568 and the new remainder 199, and apply the division lemma to get
568 = 199 x 2 + 170
We consider the new divisor 199 and the new remainder 170,and apply the division lemma to get
199 = 170 x 1 + 29
We consider the new divisor 170 and the new remainder 29,and apply the division lemma to get
170 = 29 x 5 + 25
We consider the new divisor 29 and the new remainder 25,and apply the division lemma to get
29 = 25 x 1 + 4
We consider the new divisor 25 and the new remainder 4,and apply the division lemma to get
25 = 4 x 6 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 767 and 6704 is 1
Notice that 1 = HCF(4,1) = HCF(25,4) = HCF(29,25) = HCF(170,29) = HCF(199,170) = HCF(568,199) = HCF(767,568) = HCF(6704,767) .
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Frequently Asked Questions on HCF of 767, 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 767, 6704?
Answer: HCF of 767, 6704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 767, 6704 using Euclid's Algorithm?
Answer: For arbitrary numbers 767, 6704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.