Highest Common Factor of 412, 6928 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, 6928 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 6928 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, 6928 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, 6928 is 4.
HCF(412, 6928) = 4
HCF of 412, 6928 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, 6928 is 4.
Highest Common Factor of 412,6928 is 4
Step 1: Since 6928 > 412, we apply the division lemma to 6928 and 412, to get
6928 = 412 x 16 + 336
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 336 and 412, to get
412 = 336 x 1 + 76
Step 3: We consider the new divisor 336 and the new remainder 76, and apply the division lemma to get
336 = 76 x 4 + 32
We consider the new divisor 76 and the new remainder 32,and apply the division lemma to get
76 = 32 x 2 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 6928 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(76,32) = HCF(336,76) = HCF(412,336) = HCF(6928,412) .
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Frequently Asked Questions on HCF of 412, 6928 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, 6928?
Answer: HCF of 412, 6928 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 6928 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 6928 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.