Highest Common Factor of 905, 8421, 9675 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 905, 8421, 9675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 8421, 9675 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 905, 8421, 9675 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 905, 8421, 9675 is 1.
HCF(905, 8421, 9675) = 1
HCF of 905, 8421, 9675 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 8421, 9675 is 1.
Highest Common Factor of 905,8421,9675 is 1
Step 1: Since 8421 > 905, we apply the division lemma to 8421 and 905, to get
8421 = 905 x 9 + 276
Step 2: Since the reminder 905 ≠ 0, we apply division lemma to 276 and 905, to get
905 = 276 x 3 + 77
Step 3: We consider the new divisor 276 and the new remainder 77, and apply the division lemma to get
276 = 77 x 3 + 45
We consider the new divisor 77 and the new remainder 45,and apply the division lemma to get
77 = 45 x 1 + 32
We consider the new divisor 45 and the new remainder 32,and apply the division lemma to get
45 = 32 x 1 + 13
We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get
32 = 13 x 2 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 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 905 and 8421 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(77,45) = HCF(276,77) = HCF(905,276) = HCF(8421,905) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9675 > 1, we apply the division lemma to 9675 and 1, to get
9675 = 1 x 9675 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9675 is 1
Notice that 1 = HCF(9675,1) .
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Frequently Asked Questions on HCF of 905, 8421, 9675 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 905, 8421, 9675?
Answer: HCF of 905, 8421, 9675 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 8421, 9675 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 8421, 9675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
