Highest Common Factor of 364, 208, 677 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, 208, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 208, 677 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 364, 208, 677 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, 208, 677 is 1.
HCF(364, 208, 677) = 1
HCF of 364, 208, 677 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, 208, 677 is 1.
Highest Common Factor of 364,208,677 is 1
Step 1: Since 364 > 208, we apply the division lemma to 364 and 208, to get
364 = 208 x 1 + 156
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 156 and 208, to get
208 = 156 x 1 + 52
Step 3: We consider the new divisor 156 and the new remainder 52, and apply the division lemma to get
156 = 52 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 364 and 208 is 52
Notice that 52 = HCF(156,52) = HCF(208,156) = HCF(364,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 52, we apply the division lemma to 677 and 52, to get
677 = 52 x 13 + 1
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 1 and 52, to get
52 = 1 x 52 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 52 and 677 is 1
Notice that 1 = HCF(52,1) = HCF(677,52) .
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Frequently Asked Questions on HCF of 364, 208, 677 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, 208, 677?
Answer: HCF of 364, 208, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 208, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 208, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.