Highest Common Factor of 343, 20777 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 343, 20777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 343, 20777 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 343, 20777 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 343, 20777 is 1.
HCF(343, 20777) = 1
HCF of 343, 20777 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 343, 20777 is 1.
Highest Common Factor of 343,20777 is 1
Step 1: Since 20777 > 343, we apply the division lemma to 20777 and 343, to get
20777 = 343 x 60 + 197
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 197 and 343, to get
343 = 197 x 1 + 146
Step 3: We consider the new divisor 197 and the new remainder 146, and apply the division lemma to get
197 = 146 x 1 + 51
We consider the new divisor 146 and the new remainder 51,and apply the division lemma to get
146 = 51 x 2 + 44
We consider the new divisor 51 and the new remainder 44,and apply the division lemma to get
51 = 44 x 1 + 7
We consider the new divisor 44 and the new remainder 7,and apply the division lemma to get
44 = 7 x 6 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 20777 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(44,7) = HCF(51,44) = HCF(146,51) = HCF(197,146) = HCF(343,197) = HCF(20777,343) .
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Frequently Asked Questions on HCF of 343, 20777 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 343, 20777?
Answer: HCF of 343, 20777 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 343, 20777 using Euclid's Algorithm?
Answer: For arbitrary numbers 343, 20777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.