Highest Common Factor of 7154, 5646, 20588 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 7154, 5646, 20588 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7154, 5646, 20588 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 7154, 5646, 20588 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 7154, 5646, 20588 is 2.
HCF(7154, 5646, 20588) = 2
HCF of 7154, 5646, 20588 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7154, 5646, 20588 is 2.
Highest Common Factor of 7154,5646,20588 is 2
Step 1: Since 7154 > 5646, we apply the division lemma to 7154 and 5646, to get
7154 = 5646 x 1 + 1508
Step 2: Since the reminder 5646 ≠ 0, we apply division lemma to 1508 and 5646, to get
5646 = 1508 x 3 + 1122
Step 3: We consider the new divisor 1508 and the new remainder 1122, and apply the division lemma to get
1508 = 1122 x 1 + 386
We consider the new divisor 1122 and the new remainder 386,and apply the division lemma to get
1122 = 386 x 2 + 350
We consider the new divisor 386 and the new remainder 350,and apply the division lemma to get
386 = 350 x 1 + 36
We consider the new divisor 350 and the new remainder 36,and apply the division lemma to get
350 = 36 x 9 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 7154 and 5646 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(350,36) = HCF(386,350) = HCF(1122,386) = HCF(1508,1122) = HCF(5646,1508) = HCF(7154,5646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20588 > 2, we apply the division lemma to 20588 and 2, to get
20588 = 2 x 10294 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 20588 is 2
Notice that 2 = HCF(20588,2) .
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Frequently Asked Questions on HCF of 7154, 5646, 20588 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 7154, 5646, 20588?
Answer: HCF of 7154, 5646, 20588 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7154, 5646, 20588 using Euclid's Algorithm?
Answer: For arbitrary numbers 7154, 5646, 20588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
