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, 411 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 411 is 3 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, 411 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, 411 is 3.
HCF(642, 411) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 411 is 3.
Step 1: Since 642 > 411, we apply the division lemma to 642 and 411, to get
642 = 411 x 1 + 231
Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 231 and 411, to get
411 = 231 x 1 + 180
Step 3: We consider the new divisor 231 and the new remainder 180, and apply the division lemma to get
231 = 180 x 1 + 51
We consider the new divisor 180 and the new remainder 51,and apply the division lemma to get
180 = 51 x 3 + 27
We consider the new divisor 51 and the new remainder 27,and apply the division lemma to get
51 = 27 x 1 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 642 and 411 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(51,27) = HCF(180,51) = HCF(231,180) = HCF(411,231) = HCF(642,411) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 411?
Answer: HCF of 642, 411 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.