Highest Common Factor of 364, 686, 764 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 364, 686, 764 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 686, 764 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 364, 686, 764 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 364, 686, 764 is 2.
HCF(364, 686, 764) = 2
HCF of 364, 686, 764 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 686, 764 is 2.
Highest Common Factor of 364,686,764 is 2
Step 1: Since 686 > 364, we apply the division lemma to 686 and 364, to get
686 = 364 x 1 + 322
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 322 and 364, to get
364 = 322 x 1 + 42
Step 3: We consider the new divisor 322 and the new remainder 42, and apply the division lemma to get
322 = 42 x 7 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 364 and 686 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(322,42) = HCF(364,322) = HCF(686,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 764 > 14, we apply the division lemma to 764 and 14, to get
764 = 14 x 54 + 8
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 8 and 14, to get
14 = 8 x 1 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 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 14 and 764 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(764,14) .
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Frequently Asked Questions on HCF of 364, 686, 764 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 364, 686, 764?
Answer: HCF of 364, 686, 764 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 686, 764 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 686, 764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.