Highest Common Factor of 804, 504, 867 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 804, 504, 867 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 804, 504, 867 is 3 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 804, 504, 867 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 804, 504, 867 is 3.
HCF(804, 504, 867) = 3
HCF of 804, 504, 867 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 804, 504, 867 is 3.
Highest Common Factor of 804,504,867 is 3
Step 1: Since 804 > 504, we apply the division lemma to 804 and 504, to get
804 = 504 x 1 + 300
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 300 and 504, to get
504 = 300 x 1 + 204
Step 3: We consider the new divisor 300 and the new remainder 204, and apply the division lemma to get
300 = 204 x 1 + 96
We consider the new divisor 204 and the new remainder 96,and apply the division lemma to get
204 = 96 x 2 + 12
We consider the new divisor 96 and the new remainder 12,and apply the division lemma to get
96 = 12 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 804 and 504 is 12
Notice that 12 = HCF(96,12) = HCF(204,96) = HCF(300,204) = HCF(504,300) = HCF(804,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 867 > 12, we apply the division lemma to 867 and 12, to get
867 = 12 x 72 + 3
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 3 and 12, to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 867 is 3
Notice that 3 = HCF(12,3) = HCF(867,12) .
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Frequently Asked Questions on HCF of 804, 504, 867 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 804, 504, 867?
Answer: HCF of 804, 504, 867 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 804, 504, 867 using Euclid's Algorithm?
Answer: For arbitrary numbers 804, 504, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.