Highest Common Factor of 458, 2758, 9764 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 458, 2758, 9764 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 458, 2758, 9764 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 458, 2758, 9764 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 458, 2758, 9764 is 2.
HCF(458, 2758, 9764) = 2
HCF of 458, 2758, 9764 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 458, 2758, 9764 is 2.
Highest Common Factor of 458,2758,9764 is 2
Step 1: Since 2758 > 458, we apply the division lemma to 2758 and 458, to get
2758 = 458 x 6 + 10
Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 10 and 458, to get
458 = 10 x 45 + 8
Step 3: We consider the new divisor 10 and the new remainder 8, and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 458 and 2758 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(458,10) = HCF(2758,458) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9764 > 2, we apply the division lemma to 9764 and 2, to get
9764 = 2 x 4882 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9764 is 2
Notice that 2 = HCF(9764,2) .
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Frequently Asked Questions on HCF of 458, 2758, 9764 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 458, 2758, 9764?
Answer: HCF of 458, 2758, 9764 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 458, 2758, 9764 using Euclid's Algorithm?
Answer: For arbitrary numbers 458, 2758, 9764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.