Highest Common Factor of 426, 273, 78 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 426, 273, 78 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 426, 273, 78 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 426, 273, 78 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 426, 273, 78 is 3.
HCF(426, 273, 78) = 3
HCF of 426, 273, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 426, 273, 78 is 3.
Highest Common Factor of 426,273,78 is 3
Step 1: Since 426 > 273, we apply the division lemma to 426 and 273, to get
426 = 273 x 1 + 153
Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 153 and 273, to get
273 = 153 x 1 + 120
Step 3: We consider the new divisor 153 and the new remainder 120, and apply the division lemma to get
153 = 120 x 1 + 33
We consider the new divisor 120 and the new remainder 33,and apply the division lemma to get
120 = 33 x 3 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 426 and 273 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(120,33) = HCF(153,120) = HCF(273,153) = HCF(426,273) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 3, we apply the division lemma to 78 and 3, to get
78 = 3 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 78 is 3
Notice that 3 = HCF(78,3) .
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Frequently Asked Questions on HCF of 426, 273, 78 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 426, 273, 78?
Answer: HCF of 426, 273, 78 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 426, 273, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 426, 273, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.