Highest Common Factor of 471, 768 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 471, 768 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 768 is 3 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 471, 768 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 471, 768 is 3.
HCF(471, 768) = 3
HCF of 471, 768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 768 is 3.
Highest Common Factor of 471,768 is 3
Step 1: Since 768 > 471, we apply the division lemma to 768 and 471, to get
768 = 471 x 1 + 297
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 297 and 471, to get
471 = 297 x 1 + 174
Step 3: We consider the new divisor 297 and the new remainder 174, and apply the division lemma to get
297 = 174 x 1 + 123
We consider the new divisor 174 and the new remainder 123,and apply the division lemma to get
174 = 123 x 1 + 51
We consider the new divisor 123 and the new remainder 51,and apply the division lemma to get
123 = 51 x 2 + 21
We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get
51 = 21 x 2 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 768 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(123,51) = HCF(174,123) = HCF(297,174) = HCF(471,297) = HCF(768,471) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 471, 768 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 471, 768?
Answer: HCF of 471, 768 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 768 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.