Highest Common Factor of 5774, 7172 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 5774, 7172 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5774, 7172 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 5774, 7172 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 5774, 7172 is 2.
HCF(5774, 7172) = 2
HCF of 5774, 7172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5774, 7172 is 2.
Highest Common Factor of 5774,7172 is 2
Step 1: Since 7172 > 5774, we apply the division lemma to 7172 and 5774, to get
7172 = 5774 x 1 + 1398
Step 2: Since the reminder 5774 ≠ 0, we apply division lemma to 1398 and 5774, to get
5774 = 1398 x 4 + 182
Step 3: We consider the new divisor 1398 and the new remainder 182, and apply the division lemma to get
1398 = 182 x 7 + 124
We consider the new divisor 182 and the new remainder 124,and apply the division lemma to get
182 = 124 x 1 + 58
We consider the new divisor 124 and the new remainder 58,and apply the division lemma to get
124 = 58 x 2 + 8
We consider the new divisor 58 and the new remainder 8,and apply the division lemma to get
58 = 8 x 7 + 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 5774 and 7172 is 2
Notice that 2 = HCF(8,2) = HCF(58,8) = HCF(124,58) = HCF(182,124) = HCF(1398,182) = HCF(5774,1398) = HCF(7172,5774) .
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Frequently Asked Questions on HCF of 5774, 7172 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 5774, 7172?
Answer: HCF of 5774, 7172 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5774, 7172 using Euclid's Algorithm?
Answer: For arbitrary numbers 5774, 7172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
