Highest Common Factor of 306, 840, 428 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 306, 840, 428 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 840, 428 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 306, 840, 428 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 306, 840, 428 is 2.
HCF(306, 840, 428) = 2
HCF of 306, 840, 428 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 840, 428 is 2.
Highest Common Factor of 306,840,428 is 2
Step 1: Since 840 > 306, we apply the division lemma to 840 and 306, to get
840 = 306 x 2 + 228
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 228 and 306, to get
306 = 228 x 1 + 78
Step 3: We consider the new divisor 228 and the new remainder 78, and apply the division lemma to get
228 = 78 x 2 + 72
We consider the new divisor 78 and the new remainder 72,and apply the division lemma to get
78 = 72 x 1 + 6
We consider the new divisor 72 and the new remainder 6,and apply the division lemma to get
72 = 6 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 306 and 840 is 6
Notice that 6 = HCF(72,6) = HCF(78,72) = HCF(228,78) = HCF(306,228) = HCF(840,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 428 > 6, we apply the division lemma to 428 and 6, to get
428 = 6 x 71 + 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 428 is 2
Notice that 2 = HCF(6,2) = HCF(428,6) .
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Frequently Asked Questions on HCF of 306, 840, 428 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 306, 840, 428?
Answer: HCF of 306, 840, 428 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 840, 428 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 840, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.