Highest Common Factor of 605, 8245 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 605, 8245 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 605, 8245 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 605, 8245 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 605, 8245 is 5.
HCF(605, 8245) = 5
HCF of 605, 8245 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 605, 8245 is 5.
Highest Common Factor of 605,8245 is 5
Step 1: Since 8245 > 605, we apply the division lemma to 8245 and 605, to get
8245 = 605 x 13 + 380
Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 380 and 605, to get
605 = 380 x 1 + 225
Step 3: We consider the new divisor 380 and the new remainder 225, and apply the division lemma to get
380 = 225 x 1 + 155
We consider the new divisor 225 and the new remainder 155,and apply the division lemma to get
225 = 155 x 1 + 70
We consider the new divisor 155 and the new remainder 70,and apply the division lemma to get
155 = 70 x 2 + 15
We consider the new divisor 70 and the new remainder 15,and apply the division lemma to get
70 = 15 x 4 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 605 and 8245 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(70,15) = HCF(155,70) = HCF(225,155) = HCF(380,225) = HCF(605,380) = HCF(8245,605) .
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Frequently Asked Questions on HCF of 605, 8245 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 605, 8245?
Answer: HCF of 605, 8245 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 605, 8245 using Euclid's Algorithm?
Answer: For arbitrary numbers 605, 8245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.