Highest Common Factor of 51, 69, 138 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 51, 69, 138 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 51, 69, 138 is 3 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 51, 69, 138 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 51, 69, 138 is 3.
HCF(51, 69, 138) = 3
HCF of 51, 69, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 51, 69, 138 is 3.
Highest Common Factor of 51,69,138 is 3
Step 1: Since 69 > 51, we apply the division lemma to 69 and 51, to get
69 = 51 x 1 + 18
Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 18 and 51, to get
51 = 18 x 2 + 15
Step 3: We consider the new divisor 18 and the new remainder 15, and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 51 and 69 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(69,51) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 3, we apply the division lemma to 138 and 3, to get
138 = 3 x 46 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 138 is 3
Notice that 3 = HCF(138,3) .
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Frequently Asked Questions on HCF of 51, 69, 138 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 51, 69, 138?
Answer: HCF of 51, 69, 138 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 51, 69, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 51, 69, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.