Highest Common Factor of 419, 692 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 419, 692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 419, 692 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 419, 692 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 419, 692 is 1.
HCF(419, 692) = 1
HCF of 419, 692 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 419, 692 is 1.
Highest Common Factor of 419,692 is 1
Step 1: Since 692 > 419, we apply the division lemma to 692 and 419, to get
692 = 419 x 1 + 273
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 273 and 419, to get
419 = 273 x 1 + 146
Step 3: We consider the new divisor 273 and the new remainder 146, and apply the division lemma to get
273 = 146 x 1 + 127
We consider the new divisor 146 and the new remainder 127,and apply the division lemma to get
146 = 127 x 1 + 19
We consider the new divisor 127 and the new remainder 19,and apply the division lemma to get
127 = 19 x 6 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 692 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(127,19) = HCF(146,127) = HCF(273,146) = HCF(419,273) = HCF(692,419) .
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Frequently Asked Questions on HCF of 419, 692 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 419, 692?
Answer: HCF of 419, 692 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 419, 692 using Euclid's Algorithm?
Answer: For arbitrary numbers 419, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.