Highest Common Factor of 457, 298, 908 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 457, 298, 908 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 298, 908 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 457, 298, 908 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 457, 298, 908 is 1.
HCF(457, 298, 908) = 1
HCF of 457, 298, 908 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 298, 908 is 1.
Highest Common Factor of 457,298,908 is 1
Step 1: Since 457 > 298, we apply the division lemma to 457 and 298, to get
457 = 298 x 1 + 159
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 159 and 298, to get
298 = 159 x 1 + 139
Step 3: We consider the new divisor 159 and the new remainder 139, and apply the division lemma to get
159 = 139 x 1 + 20
We consider the new divisor 139 and the new remainder 20,and apply the division lemma to get
139 = 20 x 6 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 298 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(139,20) = HCF(159,139) = HCF(298,159) = HCF(457,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 908 > 1, we apply the division lemma to 908 and 1, to get
908 = 1 x 908 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 908 is 1
Notice that 1 = HCF(908,1) .
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Frequently Asked Questions on HCF of 457, 298, 908 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 457, 298, 908?
Answer: HCF of 457, 298, 908 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 298, 908 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 298, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
