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 641, 3105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 641, 3105 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 641, 3105 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 641, 3105 is 1.
HCF(641, 3105) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 641, 3105 is 1.
Step 1: Since 3105 > 641, we apply the division lemma to 3105 and 641, to get
3105 = 641 x 4 + 541
Step 2: Since the reminder 641 ≠ 0, we apply division lemma to 541 and 641, to get
641 = 541 x 1 + 100
Step 3: We consider the new divisor 541 and the new remainder 100, and apply the division lemma to get
541 = 100 x 5 + 41
We consider the new divisor 100 and the new remainder 41,and apply the division lemma to get
100 = 41 x 2 + 18
We consider the new divisor 41 and the new remainder 18,and apply the division lemma to get
41 = 18 x 2 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 641 and 3105 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(41,18) = HCF(100,41) = HCF(541,100) = HCF(641,541) = HCF(3105,641) .
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 641, 3105?
Answer: HCF of 641, 3105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 641, 3105 using Euclid's Algorithm?
Answer: For arbitrary numbers 641, 3105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.