Highest Common Factor of 612, 784, 670 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 612, 784, 670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 784, 670 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 612, 784, 670 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 612, 784, 670 is 2.
HCF(612, 784, 670) = 2
HCF of 612, 784, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 784, 670 is 2.
Highest Common Factor of 612,784,670 is 2
Step 1: Since 784 > 612, we apply the division lemma to 784 and 612, to get
784 = 612 x 1 + 172
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 172 and 612, to get
612 = 172 x 3 + 96
Step 3: We consider the new divisor 172 and the new remainder 96, and apply the division lemma to get
172 = 96 x 1 + 76
We consider the new divisor 96 and the new remainder 76,and apply the division lemma to get
96 = 76 x 1 + 20
We consider the new divisor 76 and the new remainder 20,and apply the division lemma to get
76 = 20 x 3 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 612 and 784 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(76,20) = HCF(96,76) = HCF(172,96) = HCF(612,172) = HCF(784,612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 670 > 4, we apply the division lemma to 670 and 4, to get
670 = 4 x 167 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 670 is 2
Notice that 2 = HCF(4,2) = HCF(670,4) .
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Frequently Asked Questions on HCF of 612, 784, 670 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 612, 784, 670?
Answer: HCF of 612, 784, 670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 784, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 784, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.