Highest Common Factor of 3662, 6742 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 3662, 6742 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3662, 6742 is 2 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 3662, 6742 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 3662, 6742 is 2.
HCF(3662, 6742) = 2
HCF of 3662, 6742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3662, 6742 is 2.
Highest Common Factor of 3662,6742 is 2
Step 1: Since 6742 > 3662, we apply the division lemma to 6742 and 3662, to get
6742 = 3662 x 1 + 3080
Step 2: Since the reminder 3662 ≠ 0, we apply division lemma to 3080 and 3662, to get
3662 = 3080 x 1 + 582
Step 3: We consider the new divisor 3080 and the new remainder 582, and apply the division lemma to get
3080 = 582 x 5 + 170
We consider the new divisor 582 and the new remainder 170,and apply the division lemma to get
582 = 170 x 3 + 72
We consider the new divisor 170 and the new remainder 72,and apply the division lemma to get
170 = 72 x 2 + 26
We consider the new divisor 72 and the new remainder 26,and apply the division lemma to get
72 = 26 x 2 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3662 and 6742 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(72,26) = HCF(170,72) = HCF(582,170) = HCF(3080,582) = HCF(3662,3080) = HCF(6742,3662) .
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Frequently Asked Questions on HCF of 3662, 6742 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 3662, 6742?
Answer: HCF of 3662, 6742 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3662, 6742 using Euclid's Algorithm?
Answer: For arbitrary numbers 3662, 6742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.