Highest Common Factor of 429, 312, 831 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, 312, 831 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 312, 831 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, 312, 831 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, 312, 831 is 3.
HCF(429, 312, 831) = 3
HCF of 429, 312, 831 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, 312, 831 is 3.
Highest Common Factor of 429,312,831 is 3
Step 1: Since 429 > 312, we apply the division lemma to 429 and 312, to get
429 = 312 x 1 + 117
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 117 and 312, to get
312 = 117 x 2 + 78
Step 3: We consider the new divisor 117 and the new remainder 78, and apply the division lemma to get
117 = 78 x 1 + 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 312 is 39
Notice that 39 = HCF(78,39) = HCF(117,78) = HCF(312,117) = HCF(429,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 831 > 39, we apply the division lemma to 831 and 39, to get
831 = 39 x 21 + 12
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 12 and 39, to get
39 = 12 x 3 + 3
Step 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 39 and 831 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(831,39) .
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Frequently Asked Questions on HCF of 429, 312, 831 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, 312, 831?
Answer: HCF of 429, 312, 831 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 312, 831 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 312, 831 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
