Highest Common Factor of 712, 584, 765 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 712, 584, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 584, 765 is 1 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 712, 584, 765 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 712, 584, 765 is 1.
HCF(712, 584, 765) = 1
HCF of 712, 584, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 584, 765 is 1.
Highest Common Factor of 712,584,765 is 1
Step 1: Since 712 > 584, we apply the division lemma to 712 and 584, to get
712 = 584 x 1 + 128
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 128 and 584, to get
584 = 128 x 4 + 72
Step 3: We consider the new divisor 128 and the new remainder 72, and apply the division lemma to get
128 = 72 x 1 + 56
We consider the new divisor 72 and the new remainder 56,and apply the division lemma to get
72 = 56 x 1 + 16
We consider the new divisor 56 and the new remainder 16,and apply the division lemma to get
56 = 16 x 3 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 584 is 8
Notice that 8 = HCF(16,8) = HCF(56,16) = HCF(72,56) = HCF(128,72) = HCF(584,128) = HCF(712,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 8, we apply the division lemma to 765 and 8, to get
765 = 8 x 95 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 765 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(765,8) .
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Frequently Asked Questions on HCF of 712, 584, 765 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 712, 584, 765?
Answer: HCF of 712, 584, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 584, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 584, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.