Highest Common Factor of 814, 460, 90 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 814, 460, 90 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 460, 90 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 814, 460, 90 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 814, 460, 90 is 2.
HCF(814, 460, 90) = 2
HCF of 814, 460, 90 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 460, 90 is 2.
Highest Common Factor of 814,460,90 is 2
Step 1: Since 814 > 460, we apply the division lemma to 814 and 460, to get
814 = 460 x 1 + 354
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 354 and 460, to get
460 = 354 x 1 + 106
Step 3: We consider the new divisor 354 and the new remainder 106, and apply the division lemma to get
354 = 106 x 3 + 36
We consider the new divisor 106 and the new remainder 36,and apply the division lemma to get
106 = 36 x 2 + 34
We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 814 and 460 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(106,36) = HCF(354,106) = HCF(460,354) = HCF(814,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 90 > 2, we apply the division lemma to 90 and 2, to get
90 = 2 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 90 is 2
Notice that 2 = HCF(90,2) .
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Frequently Asked Questions on HCF of 814, 460, 90 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 814, 460, 90?
Answer: HCF of 814, 460, 90 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 460, 90 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 460, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.