Highest Common Factor of 495, 8561, 8658 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 495, 8561, 8658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 495, 8561, 8658 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 495, 8561, 8658 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 495, 8561, 8658 is 1.
HCF(495, 8561, 8658) = 1
HCF of 495, 8561, 8658 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 495, 8561, 8658 is 1.
Highest Common Factor of 495,8561,8658 is 1
Step 1: Since 8561 > 495, we apply the division lemma to 8561 and 495, to get
8561 = 495 x 17 + 146
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 146 and 495, to get
495 = 146 x 3 + 57
Step 3: We consider the new divisor 146 and the new remainder 57, and apply the division lemma to get
146 = 57 x 2 + 32
We consider the new divisor 57 and the new remainder 32,and apply the division lemma to get
57 = 32 x 1 + 25
We consider the new divisor 32 and the new remainder 25,and apply the division lemma to get
32 = 25 x 1 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 495 and 8561 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(32,25) = HCF(57,32) = HCF(146,57) = HCF(495,146) = HCF(8561,495) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8658 > 1, we apply the division lemma to 8658 and 1, to get
8658 = 1 x 8658 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8658 is 1
Notice that 1 = HCF(8658,1) .
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Frequently Asked Questions on HCF of 495, 8561, 8658 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 495, 8561, 8658?
Answer: HCF of 495, 8561, 8658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 495, 8561, 8658 using Euclid's Algorithm?
Answer: For arbitrary numbers 495, 8561, 8658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
