Highest Common Factor of 4678, 8478 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 4678, 8478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4678, 8478 is 2 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 4678, 8478 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 4678, 8478 is 2.
HCF(4678, 8478) = 2
HCF of 4678, 8478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4678, 8478 is 2.
Highest Common Factor of 4678,8478 is 2
Step 1: Since 8478 > 4678, we apply the division lemma to 8478 and 4678, to get
8478 = 4678 x 1 + 3800
Step 2: Since the reminder 4678 ≠ 0, we apply division lemma to 3800 and 4678, to get
4678 = 3800 x 1 + 878
Step 3: We consider the new divisor 3800 and the new remainder 878, and apply the division lemma to get
3800 = 878 x 4 + 288
We consider the new divisor 878 and the new remainder 288,and apply the division lemma to get
878 = 288 x 3 + 14
We consider the new divisor 288 and the new remainder 14,and apply the division lemma to get
288 = 14 x 20 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4678 and 8478 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(288,14) = HCF(878,288) = HCF(3800,878) = HCF(4678,3800) = HCF(8478,4678) .
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Frequently Asked Questions on HCF of 4678, 8478 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 4678, 8478?
Answer: HCF of 4678, 8478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4678, 8478 using Euclid's Algorithm?
Answer: For arbitrary numbers 4678, 8478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.