Highest Common Factor of 138, 6018, 7120 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 138, 6018, 7120 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 6018, 7120 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 138, 6018, 7120 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 138, 6018, 7120 is 2.
HCF(138, 6018, 7120) = 2
HCF of 138, 6018, 7120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 6018, 7120 is 2.
Highest Common Factor of 138,6018,7120 is 2
Step 1: Since 6018 > 138, we apply the division lemma to 6018 and 138, to get
6018 = 138 x 43 + 84
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 84 and 138, to get
138 = 84 x 1 + 54
Step 3: We consider the new divisor 84 and the new remainder 54, and apply the division lemma to get
84 = 54 x 1 + 30
We consider the new divisor 54 and the new remainder 30,and apply the division lemma to get
54 = 30 x 1 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 138 and 6018 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(84,54) = HCF(138,84) = HCF(6018,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7120 > 6, we apply the division lemma to 7120 and 6, to get
7120 = 6 x 1186 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 7120 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(7120,6) .
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Frequently Asked Questions on HCF of 138, 6018, 7120 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 138, 6018, 7120?
Answer: HCF of 138, 6018, 7120 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 6018, 7120 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 6018, 7120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.