Highest Common Factor of 720, 6986, 3438 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 720, 6986, 3438 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 6986, 3438 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 720, 6986, 3438 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 720, 6986, 3438 is 2.
HCF(720, 6986, 3438) = 2
HCF of 720, 6986, 3438 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 6986, 3438 is 2.
Highest Common Factor of 720,6986,3438 is 2
Step 1: Since 6986 > 720, we apply the division lemma to 6986 and 720, to get
6986 = 720 x 9 + 506
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 506 and 720, to get
720 = 506 x 1 + 214
Step 3: We consider the new divisor 506 and the new remainder 214, and apply the division lemma to get
506 = 214 x 2 + 78
We consider the new divisor 214 and the new remainder 78,and apply the division lemma to get
214 = 78 x 2 + 58
We consider the new divisor 78 and the new remainder 58,and apply the division lemma to get
78 = 58 x 1 + 20
We consider the new divisor 58 and the new remainder 20,and apply the division lemma to get
58 = 20 x 2 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 720 and 6986 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(58,20) = HCF(78,58) = HCF(214,78) = HCF(506,214) = HCF(720,506) = HCF(6986,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3438 > 2, we apply the division lemma to 3438 and 2, to get
3438 = 2 x 1719 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 3438 is 2
Notice that 2 = HCF(3438,2) .
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Frequently Asked Questions on HCF of 720, 6986, 3438 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 720, 6986, 3438?
Answer: HCF of 720, 6986, 3438 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 6986, 3438 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 6986, 3438 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.