Highest Common Factor of 716, 382, 578 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 716, 382, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 382, 578 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 716, 382, 578 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 716, 382, 578 is 2.
HCF(716, 382, 578) = 2
HCF of 716, 382, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 382, 578 is 2.
Highest Common Factor of 716,382,578 is 2
Step 1: Since 716 > 382, we apply the division lemma to 716 and 382, to get
716 = 382 x 1 + 334
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 334 and 382, to get
382 = 334 x 1 + 48
Step 3: We consider the new divisor 334 and the new remainder 48, and apply the division lemma to get
334 = 48 x 6 + 46
We consider the new divisor 48 and the new remainder 46,and apply the division lemma to get
48 = 46 x 1 + 2
We consider the new divisor 46 and the new remainder 2,and apply the division lemma to get
46 = 2 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 716 and 382 is 2
Notice that 2 = HCF(46,2) = HCF(48,46) = HCF(334,48) = HCF(382,334) = HCF(716,382) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 578 > 2, we apply the division lemma to 578 and 2, to get
578 = 2 x 289 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 578 is 2
Notice that 2 = HCF(578,2) .
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Frequently Asked Questions on HCF of 716, 382, 578 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 716, 382, 578?
Answer: HCF of 716, 382, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 382, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 382, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.