Highest Common Factor of 338, 577, 686 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 338, 577, 686 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 577, 686 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 338, 577, 686 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 338, 577, 686 is 1.
HCF(338, 577, 686) = 1
HCF of 338, 577, 686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 577, 686 is 1.
Highest Common Factor of 338,577,686 is 1
Step 1: Since 577 > 338, we apply the division lemma to 577 and 338, to get
577 = 338 x 1 + 239
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 239 and 338, to get
338 = 239 x 1 + 99
Step 3: We consider the new divisor 239 and the new remainder 99, and apply the division lemma to get
239 = 99 x 2 + 41
We consider the new divisor 99 and the new remainder 41,and apply the division lemma to get
99 = 41 x 2 + 17
We consider the new divisor 41 and the new remainder 17,and apply the division lemma to get
41 = 17 x 2 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 338 and 577 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(41,17) = HCF(99,41) = HCF(239,99) = HCF(338,239) = HCF(577,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 1, we apply the division lemma to 686 and 1, to get
686 = 1 x 686 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 686 is 1
Notice that 1 = HCF(686,1) .
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Frequently Asked Questions on HCF of 338, 577, 686 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 338, 577, 686?
Answer: HCF of 338, 577, 686 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 577, 686 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 577, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.