Highest Common Factor of 3138, 7298 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 3138, 7298 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3138, 7298 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 3138, 7298 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 3138, 7298 is 2.
HCF(3138, 7298) = 2
HCF of 3138, 7298 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3138, 7298 is 2.
Highest Common Factor of 3138,7298 is 2
Step 1: Since 7298 > 3138, we apply the division lemma to 7298 and 3138, to get
7298 = 3138 x 2 + 1022
Step 2: Since the reminder 3138 ≠ 0, we apply division lemma to 1022 and 3138, to get
3138 = 1022 x 3 + 72
Step 3: We consider the new divisor 1022 and the new remainder 72, and apply the division lemma to get
1022 = 72 x 14 + 14
We consider the new divisor 72 and the new remainder 14,and apply the division lemma to get
72 = 14 x 5 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3138 and 7298 is 2
Notice that 2 = HCF(14,2) = HCF(72,14) = HCF(1022,72) = HCF(3138,1022) = HCF(7298,3138) .
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Frequently Asked Questions on HCF of 3138, 7298 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 3138, 7298?
Answer: HCF of 3138, 7298 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3138, 7298 using Euclid's Algorithm?
Answer: For arbitrary numbers 3138, 7298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.