Highest Common Factor of 8666, 6506, 75066 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 8666, 6506, 75066 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8666, 6506, 75066 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 8666, 6506, 75066 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 8666, 6506, 75066 is 2.
HCF(8666, 6506, 75066) = 2
HCF of 8666, 6506, 75066 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8666, 6506, 75066 is 2.
Highest Common Factor of 8666,6506,75066 is 2
Step 1: Since 8666 > 6506, we apply the division lemma to 8666 and 6506, to get
8666 = 6506 x 1 + 2160
Step 2: Since the reminder 6506 ≠ 0, we apply division lemma to 2160 and 6506, to get
6506 = 2160 x 3 + 26
Step 3: We consider the new divisor 2160 and the new remainder 26, and apply the division lemma to get
2160 = 26 x 83 + 2
We consider the new divisor 26 and the new remainder 2, and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8666 and 6506 is 2
Notice that 2 = HCF(26,2) = HCF(2160,26) = HCF(6506,2160) = HCF(8666,6506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75066 > 2, we apply the division lemma to 75066 and 2, to get
75066 = 2 x 37533 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 75066 is 2
Notice that 2 = HCF(75066,2) .
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Frequently Asked Questions on HCF of 8666, 6506, 75066 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 8666, 6506, 75066?
Answer: HCF of 8666, 6506, 75066 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8666, 6506, 75066 using Euclid's Algorithm?
Answer: For arbitrary numbers 8666, 6506, 75066 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.