Highest Common Factor of 299, 529, 412 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 299, 529, 412 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 299, 529, 412 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 299, 529, 412 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 299, 529, 412 is 1.
HCF(299, 529, 412) = 1
HCF of 299, 529, 412 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 299, 529, 412 is 1.
Highest Common Factor of 299,529,412 is 1
Step 1: Since 529 > 299, we apply the division lemma to 529 and 299, to get
529 = 299 x 1 + 230
Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 230 and 299, to get
299 = 230 x 1 + 69
Step 3: We consider the new divisor 230 and the new remainder 69, and apply the division lemma to get
230 = 69 x 3 + 23
We consider the new divisor 69 and the new remainder 23, and apply the division lemma to get
69 = 23 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 299 and 529 is 23
Notice that 23 = HCF(69,23) = HCF(230,69) = HCF(299,230) = HCF(529,299) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 412 > 23, we apply the division lemma to 412 and 23, to get
412 = 23 x 17 + 21
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 21 and 23, to get
23 = 21 x 1 + 2
Step 3: We consider the new divisor 21 and the new remainder 2, and apply the division lemma to get
21 = 2 x 10 + 1
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 23 and 412 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(412,23) .
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Frequently Asked Questions on HCF of 299, 529, 412 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 299, 529, 412?
Answer: HCF of 299, 529, 412 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 299, 529, 412 using Euclid's Algorithm?
Answer: For arbitrary numbers 299, 529, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
