Highest Common Factor of 810, 504, 916 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 810, 504, 916 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 810, 504, 916 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 810, 504, 916 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 810, 504, 916 is 2.
HCF(810, 504, 916) = 2
HCF of 810, 504, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 810, 504, 916 is 2.
Highest Common Factor of 810,504,916 is 2
Step 1: Since 810 > 504, we apply the division lemma to 810 and 504, to get
810 = 504 x 1 + 306
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 306 and 504, to get
504 = 306 x 1 + 198
Step 3: We consider the new divisor 306 and the new remainder 198, and apply the division lemma to get
306 = 198 x 1 + 108
We consider the new divisor 198 and the new remainder 108,and apply the division lemma to get
198 = 108 x 1 + 90
We consider the new divisor 108 and the new remainder 90,and apply the division lemma to get
108 = 90 x 1 + 18
We consider the new divisor 90 and the new remainder 18,and apply the division lemma to get
90 = 18 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 810 and 504 is 18
Notice that 18 = HCF(90,18) = HCF(108,90) = HCF(198,108) = HCF(306,198) = HCF(504,306) = HCF(810,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 18, we apply the division lemma to 916 and 18, to get
916 = 18 x 50 + 16
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 16 and 18, to get
18 = 16 x 1 + 2
Step 3: We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 916 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(916,18) .
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Frequently Asked Questions on HCF of 810, 504, 916 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 810, 504, 916?
Answer: HCF of 810, 504, 916 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 810, 504, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 810, 504, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.