Highest Common Factor of 865, 502, 654 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, 502, 654 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 502, 654 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 865, 502, 654 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, 502, 654 is 1.
HCF(865, 502, 654) = 1
HCF of 865, 502, 654 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, 502, 654 is 1.
Highest Common Factor of 865,502,654 is 1
Step 1: Since 865 > 502, we apply the division lemma to 865 and 502, to get
865 = 502 x 1 + 363
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 363 and 502, to get
502 = 363 x 1 + 139
Step 3: We consider the new divisor 363 and the new remainder 139, and apply the division lemma to get
363 = 139 x 2 + 85
We consider the new divisor 139 and the new remainder 85,and apply the division lemma to get
139 = 85 x 1 + 54
We consider the new divisor 85 and the new remainder 54,and apply the division lemma to get
85 = 54 x 1 + 31
We consider the new divisor 54 and the new remainder 31,and apply the division lemma to get
54 = 31 x 1 + 23
We consider the new divisor 31 and the new remainder 23,and apply the division lemma to get
31 = 23 x 1 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 865 and 502 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(54,31) = HCF(85,54) = HCF(139,85) = HCF(363,139) = HCF(502,363) = HCF(865,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get
654 = 1 x 654 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1
Notice that 1 = HCF(654,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 865, 502, 654 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, 502, 654?
Answer: HCF of 865, 502, 654 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 502, 654 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 502, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.