Highest Common Factor of 709, 421, 51 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 709, 421, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 421, 51 is 1 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 709, 421, 51 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 709, 421, 51 is 1.
HCF(709, 421, 51) = 1
HCF of 709, 421, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 421, 51 is 1.
Highest Common Factor of 709,421,51 is 1
Step 1: Since 709 > 421, we apply the division lemma to 709 and 421, to get
709 = 421 x 1 + 288
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 288 and 421, to get
421 = 288 x 1 + 133
Step 3: We consider the new divisor 288 and the new remainder 133, and apply the division lemma to get
288 = 133 x 2 + 22
We consider the new divisor 133 and the new remainder 22,and apply the division lemma to get
133 = 22 x 6 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 421 is 1
Notice that 1 = HCF(22,1) = HCF(133,22) = HCF(288,133) = HCF(421,288) = HCF(709,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1
Notice that 1 = HCF(51,1) .
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Frequently Asked Questions on HCF of 709, 421, 51 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 709, 421, 51?
Answer: HCF of 709, 421, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 421, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 421, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
