Highest Common Factor of 705, 6571 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 705, 6571 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 6571 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 705, 6571 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 705, 6571 is 1.
HCF(705, 6571) = 1
HCF of 705, 6571 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 6571 is 1.
Highest Common Factor of 705,6571 is 1
Step 1: Since 6571 > 705, we apply the division lemma to 6571 and 705, to get
6571 = 705 x 9 + 226
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 226 and 705, to get
705 = 226 x 3 + 27
Step 3: We consider the new divisor 226 and the new remainder 27, and apply the division lemma to get
226 = 27 x 8 + 10
We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get
27 = 10 x 2 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 6571 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(226,27) = HCF(705,226) = HCF(6571,705) .
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Frequently Asked Questions on HCF of 705, 6571 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 705, 6571?
Answer: HCF of 705, 6571 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 6571 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 6571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.