Highest Common Factor of 642, 709 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 642, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 709 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 642, 709 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 642, 709 is 1.
HCF(642, 709) = 1
HCF of 642, 709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 709 is 1.
Highest Common Factor of 642,709 is 1
Step 1: Since 709 > 642, we apply the division lemma to 709 and 642, to get
709 = 642 x 1 + 67
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 67 and 642, to get
642 = 67 x 9 + 39
Step 3: We consider the new divisor 67 and the new remainder 39, and apply the division lemma to get
67 = 39 x 1 + 28
We consider the new divisor 39 and the new remainder 28,and apply the division lemma to get
39 = 28 x 1 + 11
We consider the new divisor 28 and the new remainder 11,and apply the division lemma to get
28 = 11 x 2 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 642 and 709 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(28,11) = HCF(39,28) = HCF(67,39) = HCF(642,67) = HCF(709,642) .
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Frequently Asked Questions on HCF of 642, 709 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 642, 709?
Answer: HCF of 642, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.