Highest Common Factor of 538, 992 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, 992 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 538, 992 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, 992 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, 992 is 2.
HCF(538, 992) = 2
HCF of 538, 992 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, 992 is 2.
Highest Common Factor of 538,992 is 2
Step 1: Since 992 > 538, we apply the division lemma to 992 and 538, to get
992 = 538 x 1 + 454
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 454 and 538, to get
538 = 454 x 1 + 84
Step 3: We consider the new divisor 454 and the new remainder 84, and apply the division lemma to get
454 = 84 x 5 + 34
We consider the new divisor 84 and the new remainder 34,and apply the division lemma to get
84 = 34 x 2 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 538 and 992 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(84,34) = HCF(454,84) = HCF(538,454) = HCF(992,538) .
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Frequently Asked Questions on HCF of 538, 992 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, 992?
Answer: HCF of 538, 992 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 538, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 538, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
