Highest Common Factor of 8102, 3568 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 8102, 3568 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8102, 3568 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 8102, 3568 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 8102, 3568 is 2.
HCF(8102, 3568) = 2
HCF of 8102, 3568 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8102, 3568 is 2.
Highest Common Factor of 8102,3568 is 2
Step 1: Since 8102 > 3568, we apply the division lemma to 8102 and 3568, to get
8102 = 3568 x 2 + 966
Step 2: Since the reminder 3568 ≠ 0, we apply division lemma to 966 and 3568, to get
3568 = 966 x 3 + 670
Step 3: We consider the new divisor 966 and the new remainder 670, and apply the division lemma to get
966 = 670 x 1 + 296
We consider the new divisor 670 and the new remainder 296,and apply the division lemma to get
670 = 296 x 2 + 78
We consider the new divisor 296 and the new remainder 78,and apply the division lemma to get
296 = 78 x 3 + 62
We consider the new divisor 78 and the new remainder 62,and apply the division lemma to get
78 = 62 x 1 + 16
We consider the new divisor 62 and the new remainder 16,and apply the division lemma to get
62 = 16 x 3 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8102 and 3568 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(62,16) = HCF(78,62) = HCF(296,78) = HCF(670,296) = HCF(966,670) = HCF(3568,966) = HCF(8102,3568) .
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Frequently Asked Questions on HCF of 8102, 3568 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 8102, 3568?
Answer: HCF of 8102, 3568 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8102, 3568 using Euclid's Algorithm?
Answer: For arbitrary numbers 8102, 3568 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
