Highest Common Factor of 663, 922, 786 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 663, 922, 786 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 922, 786 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 663, 922, 786 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 663, 922, 786 is 1.
HCF(663, 922, 786) = 1
HCF of 663, 922, 786 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 922, 786 is 1.
Highest Common Factor of 663,922,786 is 1
Step 1: Since 922 > 663, we apply the division lemma to 922 and 663, to get
922 = 663 x 1 + 259
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 259 and 663, to get
663 = 259 x 2 + 145
Step 3: We consider the new divisor 259 and the new remainder 145, and apply the division lemma to get
259 = 145 x 1 + 114
We consider the new divisor 145 and the new remainder 114,and apply the division lemma to get
145 = 114 x 1 + 31
We consider the new divisor 114 and the new remainder 31,and apply the division lemma to get
114 = 31 x 3 + 21
We consider the new divisor 31 and the new remainder 21,and apply the division lemma to get
31 = 21 x 1 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 663 and 922 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(114,31) = HCF(145,114) = HCF(259,145) = HCF(663,259) = HCF(922,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 786 > 1, we apply the division lemma to 786 and 1, to get
786 = 1 x 786 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 786 is 1
Notice that 1 = HCF(786,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 663, 922, 786 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 663, 922, 786?
Answer: HCF of 663, 922, 786 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 922, 786 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 922, 786 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
