Highest Common Factor of 412, 702, 678 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 412, 702, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 702, 678 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 412, 702, 678 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 412, 702, 678 is 2.
HCF(412, 702, 678) = 2
HCF of 412, 702, 678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 702, 678 is 2.
Highest Common Factor of 412,702,678 is 2
Step 1: Since 702 > 412, we apply the division lemma to 702 and 412, to get
702 = 412 x 1 + 290
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 290 and 412, to get
412 = 290 x 1 + 122
Step 3: We consider the new divisor 290 and the new remainder 122, and apply the division lemma to get
290 = 122 x 2 + 46
We consider the new divisor 122 and the new remainder 46,and apply the division lemma to get
122 = 46 x 2 + 30
We consider the new divisor 46 and the new remainder 30,and apply the division lemma to get
46 = 30 x 1 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 702 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(46,30) = HCF(122,46) = HCF(290,122) = HCF(412,290) = HCF(702,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 2, we apply the division lemma to 678 and 2, to get
678 = 2 x 339 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 678 is 2
Notice that 2 = HCF(678,2) .
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Frequently Asked Questions on HCF of 412, 702, 678 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 412, 702, 678?
Answer: HCF of 412, 702, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 702, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 702, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.