Highest Common Factor of 408, 690, 711 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 408, 690, 711 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 690, 711 is 3 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 408, 690, 711 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 408, 690, 711 is 3.
HCF(408, 690, 711) = 3
HCF of 408, 690, 711 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 690, 711 is 3.
Highest Common Factor of 408,690,711 is 3
Step 1: Since 690 > 408, we apply the division lemma to 690 and 408, to get
690 = 408 x 1 + 282
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 282 and 408, to get
408 = 282 x 1 + 126
Step 3: We consider the new divisor 282 and the new remainder 126, and apply the division lemma to get
282 = 126 x 2 + 30
We consider the new divisor 126 and the new remainder 30,and apply the division lemma to get
126 = 30 x 4 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 408 and 690 is 6
Notice that 6 = HCF(30,6) = HCF(126,30) = HCF(282,126) = HCF(408,282) = HCF(690,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 711 > 6, we apply the division lemma to 711 and 6, to get
711 = 6 x 118 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 711 is 3
Notice that 3 = HCF(6,3) = HCF(711,6) .
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Frequently Asked Questions on HCF of 408, 690, 711 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 408, 690, 711?
Answer: HCF of 408, 690, 711 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 690, 711 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 690, 711 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.