Highest Common Factor of 584, 960 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, 960 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 960 is 8 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, 960 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, 960 is 8.
HCF(584, 960) = 8
HCF of 584, 960 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, 960 is 8.
Highest Common Factor of 584,960 is 8
Step 1: Since 960 > 584, we apply the division lemma to 960 and 584, to get
960 = 584 x 1 + 376
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 376 and 584, to get
584 = 376 x 1 + 208
Step 3: We consider the new divisor 376 and the new remainder 208, and apply the division lemma to get
376 = 208 x 1 + 168
We consider the new divisor 208 and the new remainder 168,and apply the division lemma to get
208 = 168 x 1 + 40
We consider the new divisor 168 and the new remainder 40,and apply the division lemma to get
168 = 40 x 4 + 8
We consider the new divisor 40 and the new remainder 8,and apply the division lemma to get
40 = 8 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 584 and 960 is 8
Notice that 8 = HCF(40,8) = HCF(168,40) = HCF(208,168) = HCF(376,208) = HCF(584,376) = HCF(960,584) .
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Frequently Asked Questions on HCF of 584, 960 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, 960?
Answer: HCF of 584, 960 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 960 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.