Highest Common Factor of 343, 54759 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, 54759 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 343, 54759 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, 54759 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, 54759 is 1.
HCF(343, 54759) = 1
HCF of 343, 54759 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, 54759 is 1.
Highest Common Factor of 343,54759 is 1
Step 1: Since 54759 > 343, we apply the division lemma to 54759 and 343, to get
54759 = 343 x 159 + 222
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 222 and 343, to get
343 = 222 x 1 + 121
Step 3: We consider the new divisor 222 and the new remainder 121, and apply the division lemma to get
222 = 121 x 1 + 101
We consider the new divisor 121 and the new remainder 101,and apply the division lemma to get
121 = 101 x 1 + 20
We consider the new divisor 101 and the new remainder 20,and apply the division lemma to get
101 = 20 x 5 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 54759 is 1
Notice that 1 = HCF(20,1) = HCF(101,20) = HCF(121,101) = HCF(222,121) = HCF(343,222) = HCF(54759,343) .
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Frequently Asked Questions on HCF of 343, 54759 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, 54759?
Answer: HCF of 343, 54759 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 343, 54759 using Euclid's Algorithm?
Answer: For arbitrary numbers 343, 54759 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
