Highest Common Factor of 495, 8720 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, 8720 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 495, 8720 is 5 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, 8720 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, 8720 is 5.
HCF(495, 8720) = 5
HCF of 495, 8720 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, 8720 is 5.
Highest Common Factor of 495,8720 is 5
Step 1: Since 8720 > 495, we apply the division lemma to 8720 and 495, to get
8720 = 495 x 17 + 305
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 305 and 495, to get
495 = 305 x 1 + 190
Step 3: We consider the new divisor 305 and the new remainder 190, and apply the division lemma to get
305 = 190 x 1 + 115
We consider the new divisor 190 and the new remainder 115,and apply the division lemma to get
190 = 115 x 1 + 75
We consider the new divisor 115 and the new remainder 75,and apply the division lemma to get
115 = 75 x 1 + 40
We consider the new divisor 75 and the new remainder 40,and apply the division lemma to get
75 = 40 x 1 + 35
We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 495 and 8720 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(115,75) = HCF(190,115) = HCF(305,190) = HCF(495,305) = HCF(8720,495) .
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Frequently Asked Questions on HCF of 495, 8720 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, 8720?
Answer: HCF of 495, 8720 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 495, 8720 using Euclid's Algorithm?
Answer: For arbitrary numbers 495, 8720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.