Highest Common Factor of 428, 111, 353 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, 111, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 111, 353 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, 111, 353 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, 111, 353 is 1.
HCF(428, 111, 353) = 1
HCF of 428, 111, 353 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, 111, 353 is 1.
Highest Common Factor of 428,111,353 is 1
Step 1: Since 428 > 111, we apply the division lemma to 428 and 111, to get
428 = 111 x 3 + 95
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 95 and 111, to get
111 = 95 x 1 + 16
Step 3: We consider the new divisor 95 and the new remainder 16, and apply the division lemma to get
95 = 16 x 5 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 428 and 111 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(95,16) = HCF(111,95) = HCF(428,111) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 353 > 1, we apply the division lemma to 353 and 1, to get
353 = 1 x 353 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 353 is 1
Notice that 1 = HCF(353,1) .
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Frequently Asked Questions on HCF of 428, 111, 353 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, 111, 353?
Answer: HCF of 428, 111, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 111, 353 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 111, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.