Highest Common Factor of 584, 718 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 584, 718 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 718 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 584, 718 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 584, 718 is 2.
HCF(584, 718) = 2
HCF of 584, 718 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 584, 718 is 2.
Highest Common Factor of 584,718 is 2
Step 1: Since 718 > 584, we apply the division lemma to 718 and 584, to get
718 = 584 x 1 + 134
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 134 and 584, to get
584 = 134 x 4 + 48
Step 3: We consider the new divisor 134 and the new remainder 48, and apply the division lemma to get
134 = 48 x 2 + 38
We consider the new divisor 48 and the new remainder 38,and apply the division lemma to get
48 = 38 x 1 + 10
We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get
38 = 10 x 3 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 584 and 718 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(48,38) = HCF(134,48) = HCF(584,134) = HCF(718,584) .
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Frequently Asked Questions on HCF of 584, 718 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 584, 718?
Answer: HCF of 584, 718 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 718 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.