Highest Common Factor of 865, 658, 663 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, 658, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 658, 663 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, 658, 663 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, 658, 663 is 1.
HCF(865, 658, 663) = 1
HCF of 865, 658, 663 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, 658, 663 is 1.
Highest Common Factor of 865,658,663 is 1
Step 1: Since 865 > 658, we apply the division lemma to 865 and 658, to get
865 = 658 x 1 + 207
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 207 and 658, to get
658 = 207 x 3 + 37
Step 3: We consider the new divisor 207 and the new remainder 37, and apply the division lemma to get
207 = 37 x 5 + 22
We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get
37 = 22 x 1 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 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 658 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(207,37) = HCF(658,207) = HCF(865,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 663 > 1, we apply the division lemma to 663 and 1, to get
663 = 1 x 663 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 663 is 1
Notice that 1 = HCF(663,1) .
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, 658, 663 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, 658, 663?
Answer: HCF of 865, 658, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 658, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 658, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.