Highest Common Factor of 662, 382 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 662, 382 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 382 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 662, 382 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 662, 382 is 2.
HCF(662, 382) = 2
HCF of 662, 382 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 382 is 2.
Highest Common Factor of 662,382 is 2
Step 1: Since 662 > 382, we apply the division lemma to 662 and 382, to get
662 = 382 x 1 + 280
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 280 and 382, to get
382 = 280 x 1 + 102
Step 3: We consider the new divisor 280 and the new remainder 102, and apply the division lemma to get
280 = 102 x 2 + 76
We consider the new divisor 102 and the new remainder 76,and apply the division lemma to get
102 = 76 x 1 + 26
We consider the new divisor 76 and the new remainder 26,and apply the division lemma to get
76 = 26 x 2 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 662 and 382 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(76,26) = HCF(102,76) = HCF(280,102) = HCF(382,280) = HCF(662,382) .
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Frequently Asked Questions on HCF of 662, 382 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 662, 382?
Answer: HCF of 662, 382 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 382 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.