Highest Common Factor of 471, 780 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, 780 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 780 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, 780 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, 780 is 3.
HCF(471, 780) = 3
HCF of 471, 780 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, 780 is 3.
Highest Common Factor of 471,780 is 3
Step 1: Since 780 > 471, we apply the division lemma to 780 and 471, to get
780 = 471 x 1 + 309
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 309 and 471, to get
471 = 309 x 1 + 162
Step 3: We consider the new divisor 309 and the new remainder 162, and apply the division lemma to get
309 = 162 x 1 + 147
We consider the new divisor 162 and the new remainder 147,and apply the division lemma to get
162 = 147 x 1 + 15
We consider the new divisor 147 and the new remainder 15,and apply the division lemma to get
147 = 15 x 9 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 780 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(147,15) = HCF(162,147) = HCF(309,162) = HCF(471,309) = HCF(780,471) .
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Frequently Asked Questions on HCF of 471, 780 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, 780?
Answer: HCF of 471, 780 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 780 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.