Highest Common Factor of 762, 3274 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 762, 3274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 762, 3274 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 762, 3274 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 762, 3274 is 2.
HCF(762, 3274) = 2
HCF of 762, 3274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 762, 3274 is 2.
Highest Common Factor of 762,3274 is 2
Step 1: Since 3274 > 762, we apply the division lemma to 3274 and 762, to get
3274 = 762 x 4 + 226
Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 226 and 762, to get
762 = 226 x 3 + 84
Step 3: We consider the new divisor 226 and the new remainder 84, and apply the division lemma to get
226 = 84 x 2 + 58
We consider the new divisor 84 and the new remainder 58,and apply the division lemma to get
84 = 58 x 1 + 26
We consider the new divisor 58 and the new remainder 26,and apply the division lemma to get
58 = 26 x 2 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 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 762 and 3274 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(58,26) = HCF(84,58) = HCF(226,84) = HCF(762,226) = HCF(3274,762) .
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Frequently Asked Questions on HCF of 762, 3274 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 762, 3274?
Answer: HCF of 762, 3274 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 762, 3274 using Euclid's Algorithm?
Answer: For arbitrary numbers 762, 3274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.