Highest Common Factor of 772, 419 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 772, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 772, 419 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 772, 419 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 772, 419 is 1.
HCF(772, 419) = 1
HCF of 772, 419 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 772, 419 is 1.
Highest Common Factor of 772,419 is 1
Step 1: Since 772 > 419, we apply the division lemma to 772 and 419, to get
772 = 419 x 1 + 353
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 353 and 419, to get
419 = 353 x 1 + 66
Step 3: We consider the new divisor 353 and the new remainder 66, and apply the division lemma to get
353 = 66 x 5 + 23
We consider the new divisor 66 and the new remainder 23,and apply the division lemma to get
66 = 23 x 2 + 20
We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get
23 = 20 x 1 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 772 and 419 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(66,23) = HCF(353,66) = HCF(419,353) = HCF(772,419) .
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Frequently Asked Questions on HCF of 772, 419 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 772, 419?
Answer: HCF of 772, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 772, 419 using Euclid's Algorithm?
Answer: For arbitrary numbers 772, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.