Highest Common Factor of 8378, 1266 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 8378, 1266 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8378, 1266 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 8378, 1266 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 8378, 1266 is 2.
HCF(8378, 1266) = 2
HCF of 8378, 1266 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8378, 1266 is 2.
Highest Common Factor of 8378,1266 is 2
Step 1: Since 8378 > 1266, we apply the division lemma to 8378 and 1266, to get
8378 = 1266 x 6 + 782
Step 2: Since the reminder 1266 ≠ 0, we apply division lemma to 782 and 1266, to get
1266 = 782 x 1 + 484
Step 3: We consider the new divisor 782 and the new remainder 484, and apply the division lemma to get
782 = 484 x 1 + 298
We consider the new divisor 484 and the new remainder 298,and apply the division lemma to get
484 = 298 x 1 + 186
We consider the new divisor 298 and the new remainder 186,and apply the division lemma to get
298 = 186 x 1 + 112
We consider the new divisor 186 and the new remainder 112,and apply the division lemma to get
186 = 112 x 1 + 74
We consider the new divisor 112 and the new remainder 74,and apply the division lemma to get
112 = 74 x 1 + 38
We consider the new divisor 74 and the new remainder 38,and apply the division lemma to get
74 = 38 x 1 + 36
We consider the new divisor 38 and the new remainder 36,and apply the division lemma to get
38 = 36 x 1 + 2
We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8378 and 1266 is 2
Notice that 2 = HCF(36,2) = HCF(38,36) = HCF(74,38) = HCF(112,74) = HCF(186,112) = HCF(298,186) = HCF(484,298) = HCF(782,484) = HCF(1266,782) = HCF(8378,1266) .
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Frequently Asked Questions on HCF of 8378, 1266 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 8378, 1266?
Answer: HCF of 8378, 1266 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8378, 1266 using Euclid's Algorithm?
Answer: For arbitrary numbers 8378, 1266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
