Highest Common Factor of 584, 358 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, 358 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 358 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, 358 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, 358 is 2.
HCF(584, 358) = 2
HCF of 584, 358 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, 358 is 2.
Highest Common Factor of 584,358 is 2
Step 1: Since 584 > 358, we apply the division lemma to 584 and 358, to get
584 = 358 x 1 + 226
Step 2: Since the reminder 358 ≠ 0, we apply division lemma to 226 and 358, to get
358 = 226 x 1 + 132
Step 3: We consider the new divisor 226 and the new remainder 132, and apply the division lemma to get
226 = 132 x 1 + 94
We consider the new divisor 132 and the new remainder 94,and apply the division lemma to get
132 = 94 x 1 + 38
We consider the new divisor 94 and the new remainder 38,and apply the division lemma to get
94 = 38 x 2 + 18
We consider the new divisor 38 and the new remainder 18,and apply the division lemma to get
38 = 18 x 2 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 584 and 358 is 2
Notice that 2 = HCF(18,2) = HCF(38,18) = HCF(94,38) = HCF(132,94) = HCF(226,132) = HCF(358,226) = HCF(584,358) .
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Frequently Asked Questions on HCF of 584, 358 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, 358?
Answer: HCF of 584, 358 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 358 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.