Highest Common Factor of 579, 684 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 579, 684 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 579, 684 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 579, 684 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 579, 684 is 3.
HCF(579, 684) = 3
HCF of 579, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 579, 684 is 3.
Highest Common Factor of 579,684 is 3
Step 1: Since 684 > 579, we apply the division lemma to 684 and 579, to get
684 = 579 x 1 + 105
Step 2: Since the reminder 579 ≠ 0, we apply division lemma to 105 and 579, to get
579 = 105 x 5 + 54
Step 3: We consider the new divisor 105 and the new remainder 54, and apply the division lemma to get
105 = 54 x 1 + 51
We consider the new divisor 54 and the new remainder 51,and apply the division lemma to get
54 = 51 x 1 + 3
We consider the new divisor 51 and the new remainder 3,and apply the division lemma to get
51 = 3 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 579 and 684 is 3
Notice that 3 = HCF(51,3) = HCF(54,51) = HCF(105,54) = HCF(579,105) = HCF(684,579) .
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Frequently Asked Questions on HCF of 579, 684 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 579, 684?
Answer: HCF of 579, 684 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 579, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 579, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.