Highest Common Factor of 7278, 2306 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 7278, 2306 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7278, 2306 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 7278, 2306 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 7278, 2306 is 2.
HCF(7278, 2306) = 2
HCF of 7278, 2306 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7278, 2306 is 2.
Highest Common Factor of 7278,2306 is 2
Step 1: Since 7278 > 2306, we apply the division lemma to 7278 and 2306, to get
7278 = 2306 x 3 + 360
Step 2: Since the reminder 2306 ≠ 0, we apply division lemma to 360 and 2306, to get
2306 = 360 x 6 + 146
Step 3: We consider the new divisor 360 and the new remainder 146, and apply the division lemma to get
360 = 146 x 2 + 68
We consider the new divisor 146 and the new remainder 68,and apply the division lemma to get
146 = 68 x 2 + 10
We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get
68 = 10 x 6 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7278 and 2306 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(146,68) = HCF(360,146) = HCF(2306,360) = HCF(7278,2306) .
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Frequently Asked Questions on HCF of 7278, 2306 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 7278, 2306?
Answer: HCF of 7278, 2306 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7278, 2306 using Euclid's Algorithm?
Answer: For arbitrary numbers 7278, 2306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.