Highest Common Factor of 426, 738, 302 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, 738, 302 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 426, 738, 302 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 426, 738, 302 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, 738, 302 is 2.
HCF(426, 738, 302) = 2
HCF of 426, 738, 302 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, 738, 302 is 2.
Highest Common Factor of 426,738,302 is 2
Step 1: Since 738 > 426, we apply the division lemma to 738 and 426, to get
738 = 426 x 1 + 312
Step 2: Since the reminder 426 ≠ 0, we apply division lemma to 312 and 426, to get
426 = 312 x 1 + 114
Step 3: We consider the new divisor 312 and the new remainder 114, and apply the division lemma to get
312 = 114 x 2 + 84
We consider the new divisor 114 and the new remainder 84,and apply the division lemma to get
114 = 84 x 1 + 30
We consider the new divisor 84 and the new remainder 30,and apply the division lemma to get
84 = 30 x 2 + 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 426 and 738 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(84,30) = HCF(114,84) = HCF(312,114) = HCF(426,312) = HCF(738,426) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 302 > 6, we apply the division lemma to 302 and 6, to get
302 = 6 x 50 + 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 302 is 2
Notice that 2 = HCF(6,2) = HCF(302,6) .
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Frequently Asked Questions on HCF of 426, 738, 302 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, 738, 302?
Answer: HCF of 426, 738, 302 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 426, 738, 302 using Euclid's Algorithm?
Answer: For arbitrary numbers 426, 738, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.