Highest Common Factor of 1205, 6714 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 1205, 6714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1205, 6714 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 1205, 6714 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 1205, 6714 is 1.
HCF(1205, 6714) = 1
HCF of 1205, 6714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1205, 6714 is 1.
Highest Common Factor of 1205,6714 is 1
Step 1: Since 6714 > 1205, we apply the division lemma to 6714 and 1205, to get
6714 = 1205 x 5 + 689
Step 2: Since the reminder 1205 ≠ 0, we apply division lemma to 689 and 1205, to get
1205 = 689 x 1 + 516
Step 3: We consider the new divisor 689 and the new remainder 516, and apply the division lemma to get
689 = 516 x 1 + 173
We consider the new divisor 516 and the new remainder 173,and apply the division lemma to get
516 = 173 x 2 + 170
We consider the new divisor 173 and the new remainder 170,and apply the division lemma to get
173 = 170 x 1 + 3
We consider the new divisor 170 and the new remainder 3,and apply the division lemma to get
170 = 3 x 56 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 1205 and 6714 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(170,3) = HCF(173,170) = HCF(516,173) = HCF(689,516) = HCF(1205,689) = HCF(6714,1205) .
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Frequently Asked Questions on HCF of 1205, 6714 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 1205, 6714?
Answer: HCF of 1205, 6714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1205, 6714 using Euclid's Algorithm?
Answer: For arbitrary numbers 1205, 6714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.