Highest Common Factor of 322, 538 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 322, 538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 538 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 322, 538 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 322, 538 is 2.
HCF(322, 538) = 2
HCF of 322, 538 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 538 is 2.
Highest Common Factor of 322,538 is 2
Step 1: Since 538 > 322, we apply the division lemma to 538 and 322, to get
538 = 322 x 1 + 216
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 216 and 322, to get
322 = 216 x 1 + 106
Step 3: We consider the new divisor 216 and the new remainder 106, and apply the division lemma to get
216 = 106 x 2 + 4
We consider the new divisor 106 and the new remainder 4,and apply the division lemma to get
106 = 4 x 26 + 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 322 and 538 is 2
Notice that 2 = HCF(4,2) = HCF(106,4) = HCF(216,106) = HCF(322,216) = HCF(538,322) .
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Frequently Asked Questions on HCF of 322, 538 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 322, 538?
Answer: HCF of 322, 538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.