Highest Common Factor of 998, 364, 458 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 998, 364, 458 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 364, 458 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 998, 364, 458 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 998, 364, 458 is 2.
HCF(998, 364, 458) = 2
HCF of 998, 364, 458 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 364, 458 is 2.
Highest Common Factor of 998,364,458 is 2
Step 1: Since 998 > 364, we apply the division lemma to 998 and 364, to get
998 = 364 x 2 + 270
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 270 and 364, to get
364 = 270 x 1 + 94
Step 3: We consider the new divisor 270 and the new remainder 94, and apply the division lemma to get
270 = 94 x 2 + 82
We consider the new divisor 94 and the new remainder 82,and apply the division lemma to get
94 = 82 x 1 + 12
We consider the new divisor 82 and the new remainder 12,and apply the division lemma to get
82 = 12 x 6 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 364 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(82,12) = HCF(94,82) = HCF(270,94) = HCF(364,270) = HCF(998,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 458 > 2, we apply the division lemma to 458 and 2, to get
458 = 2 x 229 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 458 is 2
Notice that 2 = HCF(458,2) .
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Frequently Asked Questions on HCF of 998, 364, 458 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 998, 364, 458?
Answer: HCF of 998, 364, 458 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 364, 458 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 364, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.