Highest Common Factor of 7006, 6278 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 7006, 6278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7006, 6278 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 7006, 6278 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 7006, 6278 is 2.
HCF(7006, 6278) = 2
HCF of 7006, 6278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7006, 6278 is 2.
Highest Common Factor of 7006,6278 is 2
Step 1: Since 7006 > 6278, we apply the division lemma to 7006 and 6278, to get
7006 = 6278 x 1 + 728
Step 2: Since the reminder 6278 ≠ 0, we apply division lemma to 728 and 6278, to get
6278 = 728 x 8 + 454
Step 3: We consider the new divisor 728 and the new remainder 454, and apply the division lemma to get
728 = 454 x 1 + 274
We consider the new divisor 454 and the new remainder 274,and apply the division lemma to get
454 = 274 x 1 + 180
We consider the new divisor 274 and the new remainder 180,and apply the division lemma to get
274 = 180 x 1 + 94
We consider the new divisor 180 and the new remainder 94,and apply the division lemma to get
180 = 94 x 1 + 86
We consider the new divisor 94 and the new remainder 86,and apply the division lemma to get
94 = 86 x 1 + 8
We consider the new divisor 86 and the new remainder 8,and apply the division lemma to get
86 = 8 x 10 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7006 and 6278 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(86,8) = HCF(94,86) = HCF(180,94) = HCF(274,180) = HCF(454,274) = HCF(728,454) = HCF(6278,728) = HCF(7006,6278) .
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Frequently Asked Questions on HCF of 7006, 6278 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 7006, 6278?
Answer: HCF of 7006, 6278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7006, 6278 using Euclid's Algorithm?
Answer: For arbitrary numbers 7006, 6278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
