Highest Common Factor of 429, 780, 471 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 429, 780, 471 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 780, 471 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 429, 780, 471 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 429, 780, 471 is 3.
HCF(429, 780, 471) = 3
HCF of 429, 780, 471 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 429, 780, 471 is 3.
Highest Common Factor of 429,780,471 is 3
Step 1: Since 780 > 429, we apply the division lemma to 780 and 429, to get
780 = 429 x 1 + 351
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 351 and 429, to get
429 = 351 x 1 + 78
Step 3: We consider the new divisor 351 and the new remainder 78, and apply the division lemma to get
351 = 78 x 4 + 39
We consider the new divisor 78 and the new remainder 39, and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 429 and 780 is 39
Notice that 39 = HCF(78,39) = HCF(351,78) = HCF(429,351) = HCF(780,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 471 > 39, we apply the division lemma to 471 and 39, to get
471 = 39 x 12 + 3
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 3 and 39, to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 39 and 471 is 3
Notice that 3 = HCF(39,3) = HCF(471,39) .
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Frequently Asked Questions on HCF of 429, 780, 471 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 429, 780, 471?
Answer: HCF of 429, 780, 471 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 780, 471 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 780, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.