Highest Common Factor of 412, 2024 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 412, 2024 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 2024 is 4 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 412, 2024 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 412, 2024 is 4.
HCF(412, 2024) = 4
HCF of 412, 2024 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 2024 is 4.
Highest Common Factor of 412,2024 is 4
Step 1: Since 2024 > 412, we apply the division lemma to 2024 and 412, to get
2024 = 412 x 4 + 376
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 376 and 412, to get
412 = 376 x 1 + 36
Step 3: We consider the new divisor 376 and the new remainder 36, and apply the division lemma to get
376 = 36 x 10 + 16
We consider the new divisor 36 and the new remainder 16,and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 2024 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(376,36) = HCF(412,376) = HCF(2024,412) .
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Frequently Asked Questions on HCF of 412, 2024 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 412, 2024?
Answer: HCF of 412, 2024 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 2024 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 2024 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.