Highest Common Factor of 549, 8540 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 549, 8540 i.e. 61 the largest integer that leaves a remainder zero for all numbers.
HCF of 549, 8540 is 61 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 549, 8540 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 549, 8540 is 61.
HCF(549, 8540) = 61
HCF of 549, 8540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 549, 8540 is 61.
Highest Common Factor of 549,8540 is 61
Step 1: Since 8540 > 549, we apply the division lemma to 8540 and 549, to get
8540 = 549 x 15 + 305
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 305 and 549, to get
549 = 305 x 1 + 244
Step 3: We consider the new divisor 305 and the new remainder 244, and apply the division lemma to get
305 = 244 x 1 + 61
We consider the new divisor 244 and the new remainder 61, and apply the division lemma to get
244 = 61 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 61, the HCF of 549 and 8540 is 61
Notice that 61 = HCF(244,61) = HCF(305,244) = HCF(549,305) = HCF(8540,549) .
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Frequently Asked Questions on HCF of 549, 8540 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 549, 8540?
Answer: HCF of 549, 8540 is 61 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 549, 8540 using Euclid's Algorithm?
Answer: For arbitrary numbers 549, 8540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.