Highest Common Factor of 458, 745, 145, 96 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, 745, 145, 96 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 458, 745, 145, 96 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 458, 745, 145, 96 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, 745, 145, 96 is 1.
HCF(458, 745, 145, 96) = 1
HCF of 458, 745, 145, 96 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, 745, 145, 96 is 1.
Highest Common Factor of 458,745,145,96 is 1
Step 1: Since 745 > 458, we apply the division lemma to 745 and 458, to get
745 = 458 x 1 + 287
Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 287 and 458, to get
458 = 287 x 1 + 171
Step 3: We consider the new divisor 287 and the new remainder 171, and apply the division lemma to get
287 = 171 x 1 + 116
We consider the new divisor 171 and the new remainder 116,and apply the division lemma to get
171 = 116 x 1 + 55
We consider the new divisor 116 and the new remainder 55,and apply the division lemma to get
116 = 55 x 2 + 6
We consider the new divisor 55 and the new remainder 6,and apply the division lemma to get
55 = 6 x 9 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 458 and 745 is 1
Notice that 1 = HCF(6,1) = HCF(55,6) = HCF(116,55) = HCF(171,116) = HCF(287,171) = HCF(458,287) = HCF(745,458) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 145 > 1, we apply the division lemma to 145 and 1, to get
145 = 1 x 145 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 145 is 1
Notice that 1 = HCF(145,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 1, we apply the division lemma to 96 and 1, to get
96 = 1 x 96 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96 is 1
Notice that 1 = HCF(96,1) .
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Frequently Asked Questions on HCF of 458, 745, 145, 96 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, 745, 145, 96?
Answer: HCF of 458, 745, 145, 96 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 458, 745, 145, 96 using Euclid's Algorithm?
Answer: For arbitrary numbers 458, 745, 145, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.