Highest Common Factor of 642, 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 642, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 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 642, 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 642, 419 is 1.
HCF(642, 419) = 1
HCF of 642, 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 642, 419 is 1.
Highest Common Factor of 642,419 is 1
Step 1: Since 642 > 419, we apply the division lemma to 642 and 419, to get
642 = 419 x 1 + 223
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 223 and 419, to get
419 = 223 x 1 + 196
Step 3: We consider the new divisor 223 and the new remainder 196, and apply the division lemma to get
223 = 196 x 1 + 27
We consider the new divisor 196 and the new remainder 27,and apply the division lemma to get
196 = 27 x 7 + 7
We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get
27 = 7 x 3 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 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 642 and 419 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(196,27) = HCF(223,196) = HCF(419,223) = HCF(642,419) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 642, 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 642, 419?
Answer: HCF of 642, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 419 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.