Highest Common Factor of 454, 814, 81 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 454, 814, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 454, 814, 81 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 454, 814, 81 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 454, 814, 81 is 1.
HCF(454, 814, 81) = 1
HCF of 454, 814, 81 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 454, 814, 81 is 1.
Highest Common Factor of 454,814,81 is 1
Step 1: Since 814 > 454, we apply the division lemma to 814 and 454, to get
814 = 454 x 1 + 360
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 360 and 454, to get
454 = 360 x 1 + 94
Step 3: We consider the new divisor 360 and the new remainder 94, and apply the division lemma to get
360 = 94 x 3 + 78
We consider the new divisor 94 and the new remainder 78,and apply the division lemma to get
94 = 78 x 1 + 16
We consider the new divisor 78 and the new remainder 16,and apply the division lemma to get
78 = 16 x 4 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 454 and 814 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(78,16) = HCF(94,78) = HCF(360,94) = HCF(454,360) = HCF(814,454) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 2, we apply the division lemma to 81 and 2, to get
81 = 2 x 40 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 81 is 1
Notice that 1 = HCF(2,1) = HCF(81,2) .
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Frequently Asked Questions on HCF of 454, 814, 81 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 454, 814, 81?
Answer: HCF of 454, 814, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 454, 814, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 454, 814, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.