Highest Common Factor of 5968, 7114 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 5968, 7114 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5968, 7114 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 5968, 7114 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 5968, 7114 is 2.
HCF(5968, 7114) = 2
HCF of 5968, 7114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5968, 7114 is 2.
Highest Common Factor of 5968,7114 is 2
Step 1: Since 7114 > 5968, we apply the division lemma to 7114 and 5968, to get
7114 = 5968 x 1 + 1146
Step 2: Since the reminder 5968 ≠ 0, we apply division lemma to 1146 and 5968, to get
5968 = 1146 x 5 + 238
Step 3: We consider the new divisor 1146 and the new remainder 238, and apply the division lemma to get
1146 = 238 x 4 + 194
We consider the new divisor 238 and the new remainder 194,and apply the division lemma to get
238 = 194 x 1 + 44
We consider the new divisor 194 and the new remainder 44,and apply the division lemma to get
194 = 44 x 4 + 18
We consider the new divisor 44 and the new remainder 18,and apply the division lemma to get
44 = 18 x 2 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 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 5968 and 7114 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(44,18) = HCF(194,44) = HCF(238,194) = HCF(1146,238) = HCF(5968,1146) = HCF(7114,5968) .
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Frequently Asked Questions on HCF of 5968, 7114 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 5968, 7114?
Answer: HCF of 5968, 7114 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5968, 7114 using Euclid's Algorithm?
Answer: For arbitrary numbers 5968, 7114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
