Highest Common Factor of 538, 340 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 538, 340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 538, 340 is 2 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 538, 340 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 538, 340 is 2.
HCF(538, 340) = 2
HCF of 538, 340 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 538, 340 is 2.
Highest Common Factor of 538,340 is 2
Step 1: Since 538 > 340, we apply the division lemma to 538 and 340, to get
538 = 340 x 1 + 198
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 198 and 340, to get
340 = 198 x 1 + 142
Step 3: We consider the new divisor 198 and the new remainder 142, and apply the division lemma to get
198 = 142 x 1 + 56
We consider the new divisor 142 and the new remainder 56,and apply the division lemma to get
142 = 56 x 2 + 30
We consider the new divisor 56 and the new remainder 30,and apply the division lemma to get
56 = 30 x 1 + 26
We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get
30 = 26 x 1 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 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 538 and 340 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(56,30) = HCF(142,56) = HCF(198,142) = HCF(340,198) = HCF(538,340) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 538, 340 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 538, 340?
Answer: HCF of 538, 340 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 538, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 538, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.