Highest Common Factor of 8478, 7863 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 8478, 7863 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8478, 7863 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 8478, 7863 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 8478, 7863 is 3.
HCF(8478, 7863) = 3
HCF of 8478, 7863 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8478, 7863 is 3.
Highest Common Factor of 8478,7863 is 3
Step 1: Since 8478 > 7863, we apply the division lemma to 8478 and 7863, to get
8478 = 7863 x 1 + 615
Step 2: Since the reminder 7863 ≠ 0, we apply division lemma to 615 and 7863, to get
7863 = 615 x 12 + 483
Step 3: We consider the new divisor 615 and the new remainder 483, and apply the division lemma to get
615 = 483 x 1 + 132
We consider the new divisor 483 and the new remainder 132,and apply the division lemma to get
483 = 132 x 3 + 87
We consider the new divisor 132 and the new remainder 87,and apply the division lemma to get
132 = 87 x 1 + 45
We consider the new divisor 87 and the new remainder 45,and apply the division lemma to get
87 = 45 x 1 + 42
We consider the new divisor 45 and the new remainder 42,and apply the division lemma to get
45 = 42 x 1 + 3
We consider the new divisor 42 and the new remainder 3,and apply the division lemma to get
42 = 3 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8478 and 7863 is 3
Notice that 3 = HCF(42,3) = HCF(45,42) = HCF(87,45) = HCF(132,87) = HCF(483,132) = HCF(615,483) = HCF(7863,615) = HCF(8478,7863) .
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Frequently Asked Questions on HCF of 8478, 7863 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 8478, 7863?
Answer: HCF of 8478, 7863 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8478, 7863 using Euclid's Algorithm?
Answer: For arbitrary numbers 8478, 7863 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.