Highest Common Factor of 709, 512, 451 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, 512, 451 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 512, 451 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, 512, 451 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, 512, 451 is 1.
HCF(709, 512, 451) = 1
HCF of 709, 512, 451 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, 512, 451 is 1.
Highest Common Factor of 709,512,451 is 1
Step 1: Since 709 > 512, we apply the division lemma to 709 and 512, to get
709 = 512 x 1 + 197
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 197 and 512, to get
512 = 197 x 2 + 118
Step 3: We consider the new divisor 197 and the new remainder 118, and apply the division lemma to get
197 = 118 x 1 + 79
We consider the new divisor 118 and the new remainder 79,and apply the division lemma to get
118 = 79 x 1 + 39
We consider the new divisor 79 and the new remainder 39,and apply the division lemma to get
79 = 39 x 2 + 1
We consider the new divisor 39 and the new remainder 1,and apply the division lemma to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 512 is 1
Notice that 1 = HCF(39,1) = HCF(79,39) = HCF(118,79) = HCF(197,118) = HCF(512,197) = HCF(709,512) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 451 > 1, we apply the division lemma to 451 and 1, to get
451 = 1 x 451 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 451 is 1
Notice that 1 = HCF(451,1) .
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Frequently Asked Questions on HCF of 709, 512, 451 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, 512, 451?
Answer: HCF of 709, 512, 451 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 512, 451 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 512, 451 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.