Highest Common Factor of 8409, 6201, 85905 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 8409, 6201, 85905 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8409, 6201, 85905 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 8409, 6201, 85905 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 8409, 6201, 85905 is 3.
HCF(8409, 6201, 85905) = 3
HCF of 8409, 6201, 85905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8409, 6201, 85905 is 3.
Highest Common Factor of 8409,6201,85905 is 3
Step 1: Since 8409 > 6201, we apply the division lemma to 8409 and 6201, to get
8409 = 6201 x 1 + 2208
Step 2: Since the reminder 6201 ≠ 0, we apply division lemma to 2208 and 6201, to get
6201 = 2208 x 2 + 1785
Step 3: We consider the new divisor 2208 and the new remainder 1785, and apply the division lemma to get
2208 = 1785 x 1 + 423
We consider the new divisor 1785 and the new remainder 423,and apply the division lemma to get
1785 = 423 x 4 + 93
We consider the new divisor 423 and the new remainder 93,and apply the division lemma to get
423 = 93 x 4 + 51
We consider the new divisor 93 and the new remainder 51,and apply the division lemma to get
93 = 51 x 1 + 42
We consider the new divisor 51 and the new remainder 42,and apply the division lemma to get
51 = 42 x 1 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8409 and 6201 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(51,42) = HCF(93,51) = HCF(423,93) = HCF(1785,423) = HCF(2208,1785) = HCF(6201,2208) = HCF(8409,6201) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85905 > 3, we apply the division lemma to 85905 and 3, to get
85905 = 3 x 28635 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 85905 is 3
Notice that 3 = HCF(85905,3) .
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Frequently Asked Questions on HCF of 8409, 6201, 85905 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 8409, 6201, 85905?
Answer: HCF of 8409, 6201, 85905 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8409, 6201, 85905 using Euclid's Algorithm?
Answer: For arbitrary numbers 8409, 6201, 85905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.