Highest Common Factor of 118, 538, 343 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 118, 538, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 118, 538, 343 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 118, 538, 343 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 118, 538, 343 is 1.
HCF(118, 538, 343) = 1
HCF of 118, 538, 343 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 118, 538, 343 is 1.
Highest Common Factor of 118,538,343 is 1
Step 1: Since 538 > 118, we apply the division lemma to 538 and 118, to get
538 = 118 x 4 + 66
Step 2: Since the reminder 118 ≠ 0, we apply division lemma to 66 and 118, to get
118 = 66 x 1 + 52
Step 3: We consider the new divisor 66 and the new remainder 52, and apply the division lemma to get
66 = 52 x 1 + 14
We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get
52 = 14 x 3 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 118 and 538 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(66,52) = HCF(118,66) = HCF(538,118) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 343 > 2, we apply the division lemma to 343 and 2, to get
343 = 2 x 171 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 343 is 1
Notice that 1 = HCF(2,1) = HCF(343,2) .
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Frequently Asked Questions on HCF of 118, 538, 343 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 118, 538, 343?
Answer: HCF of 118, 538, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 118, 538, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 118, 538, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.