Highest Common Factor of 8412, 6549 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 8412, 6549 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8412, 6549 is 3 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 8412, 6549 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 8412, 6549 is 3.
HCF(8412, 6549) = 3
HCF of 8412, 6549 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8412, 6549 is 3.
Highest Common Factor of 8412,6549 is 3
Step 1: Since 8412 > 6549, we apply the division lemma to 8412 and 6549, to get
8412 = 6549 x 1 + 1863
Step 2: Since the reminder 6549 ≠ 0, we apply division lemma to 1863 and 6549, to get
6549 = 1863 x 3 + 960
Step 3: We consider the new divisor 1863 and the new remainder 960, and apply the division lemma to get
1863 = 960 x 1 + 903
We consider the new divisor 960 and the new remainder 903,and apply the division lemma to get
960 = 903 x 1 + 57
We consider the new divisor 903 and the new remainder 57,and apply the division lemma to get
903 = 57 x 15 + 48
We consider the new divisor 57 and the new remainder 48,and apply the division lemma to get
57 = 48 x 1 + 9
We consider the new divisor 48 and the new remainder 9,and apply the division lemma to get
48 = 9 x 5 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8412 and 6549 is 3
Notice that 3 = HCF(9,3) = HCF(48,9) = HCF(57,48) = HCF(903,57) = HCF(960,903) = HCF(1863,960) = HCF(6549,1863) = HCF(8412,6549) .
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Frequently Asked Questions on HCF of 8412, 6549 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 8412, 6549?
Answer: HCF of 8412, 6549 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8412, 6549 using Euclid's Algorithm?
Answer: For arbitrary numbers 8412, 6549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.