Highest Common Factor of 52, 78, 206 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 52, 78, 206 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 52, 78, 206 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 52, 78, 206 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 52, 78, 206 is 2.
HCF(52, 78, 206) = 2
HCF of 52, 78, 206 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 52, 78, 206 is 2.
Highest Common Factor of 52,78,206 is 2
Step 1: Since 78 > 52, we apply the division lemma to 78 and 52, to get
78 = 52 x 1 + 26
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 26 and 52, to get
52 = 26 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 52 and 78 is 26
Notice that 26 = HCF(52,26) = HCF(78,52) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 206 > 26, we apply the division lemma to 206 and 26, to get
206 = 26 x 7 + 24
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 24 and 26, to get
26 = 24 x 1 + 2
Step 3: We consider the new divisor 24 and the new remainder 2, and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 206 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(206,26) .
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Frequently Asked Questions on HCF of 52, 78, 206 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 52, 78, 206?
Answer: HCF of 52, 78, 206 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 52, 78, 206 using Euclid's Algorithm?
Answer: For arbitrary numbers 52, 78, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.