Highest Common Factor of 429, 501, 677 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, 501, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 501, 677 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 429, 501, 677 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, 501, 677 is 1.
HCF(429, 501, 677) = 1
HCF of 429, 501, 677 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, 501, 677 is 1.
Highest Common Factor of 429,501,677 is 1
Step 1: Since 501 > 429, we apply the division lemma to 501 and 429, to get
501 = 429 x 1 + 72
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 72 and 429, to get
429 = 72 x 5 + 69
Step 3: We consider the new divisor 72 and the new remainder 69, and apply the division lemma to get
72 = 69 x 1 + 3
We consider the new divisor 69 and the new remainder 3, and apply the division lemma to get
69 = 3 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 429 and 501 is 3
Notice that 3 = HCF(69,3) = HCF(72,69) = HCF(429,72) = HCF(501,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 3, we apply the division lemma to 677 and 3, to get
677 = 3 x 225 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 677 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(677,3) .
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Frequently Asked Questions on HCF of 429, 501, 677 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, 501, 677?
Answer: HCF of 429, 501, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 501, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 501, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.