Highest Common Factor of 2178, 7466 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 2178, 7466 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2178, 7466 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 2178, 7466 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 2178, 7466 is 2.
HCF(2178, 7466) = 2
HCF of 2178, 7466 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2178, 7466 is 2.
Highest Common Factor of 2178,7466 is 2
Step 1: Since 7466 > 2178, we apply the division lemma to 7466 and 2178, to get
7466 = 2178 x 3 + 932
Step 2: Since the reminder 2178 ≠ 0, we apply division lemma to 932 and 2178, to get
2178 = 932 x 2 + 314
Step 3: We consider the new divisor 932 and the new remainder 314, and apply the division lemma to get
932 = 314 x 2 + 304
We consider the new divisor 314 and the new remainder 304,and apply the division lemma to get
314 = 304 x 1 + 10
We consider the new divisor 304 and the new remainder 10,and apply the division lemma to get
304 = 10 x 30 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2178 and 7466 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(304,10) = HCF(314,304) = HCF(932,314) = HCF(2178,932) = HCF(7466,2178) .
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Frequently Asked Questions on HCF of 2178, 7466 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 2178, 7466?
Answer: HCF of 2178, 7466 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2178, 7466 using Euclid's Algorithm?
Answer: For arbitrary numbers 2178, 7466 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.