Highest Common Factor of 854, 697 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 854, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 697 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 854, 697 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 854, 697 is 1.
HCF(854, 697) = 1
HCF of 854, 697 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 854, 697 is 1.
Highest Common Factor of 854,697 is 1
Step 1: Since 854 > 697, we apply the division lemma to 854 and 697, to get
854 = 697 x 1 + 157
Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 157 and 697, to get
697 = 157 x 4 + 69
Step 3: We consider the new divisor 157 and the new remainder 69, and apply the division lemma to get
157 = 69 x 2 + 19
We consider the new divisor 69 and the new remainder 19,and apply the division lemma to get
69 = 19 x 3 + 12
We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get
19 = 12 x 1 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 854 and 697 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(69,19) = HCF(157,69) = HCF(697,157) = HCF(854,697) .
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Frequently Asked Questions on HCF of 854, 697 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 854, 697?
Answer: HCF of 854, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 697 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.