Highest Common Factor of 756, 868, 582 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 756, 868, 582 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 868, 582 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 756, 868, 582 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 756, 868, 582 is 2.
HCF(756, 868, 582) = 2
HCF of 756, 868, 582 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 868, 582 is 2.
Highest Common Factor of 756,868,582 is 2
Step 1: Since 868 > 756, we apply the division lemma to 868 and 756, to get
868 = 756 x 1 + 112
Step 2: Since the reminder 756 ≠ 0, we apply division lemma to 112 and 756, to get
756 = 112 x 6 + 84
Step 3: We consider the new divisor 112 and the new remainder 84, and apply the division lemma to get
112 = 84 x 1 + 28
We consider the new divisor 84 and the new remainder 28, and apply the division lemma to get
84 = 28 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 756 and 868 is 28
Notice that 28 = HCF(84,28) = HCF(112,84) = HCF(756,112) = HCF(868,756) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 582 > 28, we apply the division lemma to 582 and 28, to get
582 = 28 x 20 + 22
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 22 and 28, to get
28 = 22 x 1 + 6
Step 3: We consider the new divisor 22 and the new remainder 6, and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 28 and 582 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(582,28) .
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Frequently Asked Questions on HCF of 756, 868, 582 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 756, 868, 582?
Answer: HCF of 756, 868, 582 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 868, 582 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 868, 582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
