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 3709, 8205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3709, 8205 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 3709, 8205 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 3709, 8205 is 1.
HCF(3709, 8205) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3709, 8205 is 1.
Step 1: Since 8205 > 3709, we apply the division lemma to 8205 and 3709, to get
8205 = 3709 x 2 + 787
Step 2: Since the reminder 3709 ≠ 0, we apply division lemma to 787 and 3709, to get
3709 = 787 x 4 + 561
Step 3: We consider the new divisor 787 and the new remainder 561, and apply the division lemma to get
787 = 561 x 1 + 226
We consider the new divisor 561 and the new remainder 226,and apply the division lemma to get
561 = 226 x 2 + 109
We consider the new divisor 226 and the new remainder 109,and apply the division lemma to get
226 = 109 x 2 + 8
We consider the new divisor 109 and the new remainder 8,and apply the division lemma to get
109 = 8 x 13 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 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 3709 and 8205 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(109,8) = HCF(226,109) = HCF(561,226) = HCF(787,561) = HCF(3709,787) = HCF(8205,3709) .
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 3709, 8205?
Answer: HCF of 3709, 8205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3709, 8205 using Euclid's Algorithm?
Answer: For arbitrary numbers 3709, 8205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.