Highest Common Factor of 594, 682, 412 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 594, 682, 412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 594, 682, 412 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 594, 682, 412 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 594, 682, 412 is 2.
HCF(594, 682, 412) = 2
HCF of 594, 682, 412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 594, 682, 412 is 2.
Highest Common Factor of 594,682,412 is 2
Step 1: Since 682 > 594, we apply the division lemma to 682 and 594, to get
682 = 594 x 1 + 88
Step 2: Since the reminder 594 ≠ 0, we apply division lemma to 88 and 594, to get
594 = 88 x 6 + 66
Step 3: We consider the new divisor 88 and the new remainder 66, and apply the division lemma to get
88 = 66 x 1 + 22
We consider the new divisor 66 and the new remainder 22, and apply the division lemma to get
66 = 22 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 594 and 682 is 22
Notice that 22 = HCF(66,22) = HCF(88,66) = HCF(594,88) = HCF(682,594) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 412 > 22, we apply the division lemma to 412 and 22, to get
412 = 22 x 18 + 16
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 16 and 22, to get
22 = 16 x 1 + 6
Step 3: We consider the new divisor 16 and the new remainder 6, and apply the division lemma to get
16 = 6 x 2 + 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 22 and 412 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(412,22) .
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Frequently Asked Questions on HCF of 594, 682, 412 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 594, 682, 412?
Answer: HCF of 594, 682, 412 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 594, 682, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 594, 682, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.