Highest Common Factor of 2006, 8772 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 2006, 8772 i.e. 34 the largest integer that leaves a remainder zero for all numbers.
HCF of 2006, 8772 is 34 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 2006, 8772 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 2006, 8772 is 34.
HCF(2006, 8772) = 34
HCF of 2006, 8772 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2006, 8772 is 34.
Highest Common Factor of 2006,8772 is 34
Step 1: Since 8772 > 2006, we apply the division lemma to 8772 and 2006, to get
8772 = 2006 x 4 + 748
Step 2: Since the reminder 2006 ≠ 0, we apply division lemma to 748 and 2006, to get
2006 = 748 x 2 + 510
Step 3: We consider the new divisor 748 and the new remainder 510, and apply the division lemma to get
748 = 510 x 1 + 238
We consider the new divisor 510 and the new remainder 238,and apply the division lemma to get
510 = 238 x 2 + 34
We consider the new divisor 238 and the new remainder 34,and apply the division lemma to get
238 = 34 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 2006 and 8772 is 34
Notice that 34 = HCF(238,34) = HCF(510,238) = HCF(748,510) = HCF(2006,748) = HCF(8772,2006) .
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Frequently Asked Questions on HCF of 2006, 8772 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 2006, 8772?
Answer: HCF of 2006, 8772 is 34 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2006, 8772 using Euclid's Algorithm?
Answer: For arbitrary numbers 2006, 8772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.