Highest Common Factor of 428, 726, 375 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 428, 726, 375 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 726, 375 is 1 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 428, 726, 375 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 428, 726, 375 is 1.
HCF(428, 726, 375) = 1
HCF of 428, 726, 375 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 726, 375 is 1.
Highest Common Factor of 428,726,375 is 1
Step 1: Since 726 > 428, we apply the division lemma to 726 and 428, to get
726 = 428 x 1 + 298
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 298 and 428, to get
428 = 298 x 1 + 130
Step 3: We consider the new divisor 298 and the new remainder 130, and apply the division lemma to get
298 = 130 x 2 + 38
We consider the new divisor 130 and the new remainder 38,and apply the division lemma to get
130 = 38 x 3 + 16
We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get
38 = 16 x 2 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 428 and 726 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(130,38) = HCF(298,130) = HCF(428,298) = HCF(726,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 375 > 2, we apply the division lemma to 375 and 2, to get
375 = 2 x 187 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 375 is 1
Notice that 1 = HCF(2,1) = HCF(375,2) .
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Frequently Asked Questions on HCF of 428, 726, 375 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 428, 726, 375?
Answer: HCF of 428, 726, 375 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 726, 375 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 726, 375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
