Highest Common Factor of 5184, 7368, 12106 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 5184, 7368, 12106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5184, 7368, 12106 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 5184, 7368, 12106 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 5184, 7368, 12106 is 2.
HCF(5184, 7368, 12106) = 2
HCF of 5184, 7368, 12106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5184, 7368, 12106 is 2.
Highest Common Factor of 5184,7368,12106 is 2
Step 1: Since 7368 > 5184, we apply the division lemma to 7368 and 5184, to get
7368 = 5184 x 1 + 2184
Step 2: Since the reminder 5184 ≠ 0, we apply division lemma to 2184 and 5184, to get
5184 = 2184 x 2 + 816
Step 3: We consider the new divisor 2184 and the new remainder 816, and apply the division lemma to get
2184 = 816 x 2 + 552
We consider the new divisor 816 and the new remainder 552,and apply the division lemma to get
816 = 552 x 1 + 264
We consider the new divisor 552 and the new remainder 264,and apply the division lemma to get
552 = 264 x 2 + 24
We consider the new divisor 264 and the new remainder 24,and apply the division lemma to get
264 = 24 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 5184 and 7368 is 24
Notice that 24 = HCF(264,24) = HCF(552,264) = HCF(816,552) = HCF(2184,816) = HCF(5184,2184) = HCF(7368,5184) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12106 > 24, we apply the division lemma to 12106 and 24, to get
12106 = 24 x 504 + 10
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 10 and 24, to get
24 = 10 x 2 + 4
Step 3: 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 24 and 12106 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(12106,24) .
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Frequently Asked Questions on HCF of 5184, 7368, 12106 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 5184, 7368, 12106?
Answer: HCF of 5184, 7368, 12106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5184, 7368, 12106 using Euclid's Algorithm?
Answer: For arbitrary numbers 5184, 7368, 12106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
