Highest Common Factor of 102, 186, 278 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 102, 186, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 102, 186, 278 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 102, 186, 278 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 102, 186, 278 is 2.
HCF(102, 186, 278) = 2
HCF of 102, 186, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 102, 186, 278 is 2.
Highest Common Factor of 102,186,278 is 2
Step 1: Since 186 > 102, we apply the division lemma to 186 and 102, to get
186 = 102 x 1 + 84
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 84 and 102, to get
102 = 84 x 1 + 18
Step 3: We consider the new divisor 84 and the new remainder 18, and apply the division lemma to get
84 = 18 x 4 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 102 and 186 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(84,18) = HCF(102,84) = HCF(186,102) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 6, we apply the division lemma to 278 and 6, to get
278 = 6 x 46 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 278 is 2
Notice that 2 = HCF(6,2) = HCF(278,6) .
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Frequently Asked Questions on HCF of 102, 186, 278 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 102, 186, 278?
Answer: HCF of 102, 186, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 102, 186, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 102, 186, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.