Highest Common Factor of 865, 68035 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 865, 68035 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 68035 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 865, 68035 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 865, 68035 is 5.
HCF(865, 68035) = 5
HCF of 865, 68035 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 865, 68035 is 5.
Highest Common Factor of 865,68035 is 5
Step 1: Since 68035 > 865, we apply the division lemma to 68035 and 865, to get
68035 = 865 x 78 + 565
Step 2: Since the reminder 865 ≠ 0, we apply division lemma to 565 and 865, to get
865 = 565 x 1 + 300
Step 3: We consider the new divisor 565 and the new remainder 300, and apply the division lemma to get
565 = 300 x 1 + 265
We consider the new divisor 300 and the new remainder 265,and apply the division lemma to get
300 = 265 x 1 + 35
We consider the new divisor 265 and the new remainder 35,and apply the division lemma to get
265 = 35 x 7 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 865 and 68035 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(265,35) = HCF(300,265) = HCF(565,300) = HCF(865,565) = HCF(68035,865) .
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Frequently Asked Questions on HCF of 865, 68035 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 865, 68035?
Answer: HCF of 865, 68035 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 68035 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 68035 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
