Highest Common Factor of 804, 2714 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, 2714 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 804, 2714 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 804, 2714 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, 2714 is 2.
HCF(804, 2714) = 2
HCF of 804, 2714 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, 2714 is 2.
Highest Common Factor of 804,2714 is 2
Step 1: Since 2714 > 804, we apply the division lemma to 2714 and 804, to get
2714 = 804 x 3 + 302
Step 2: Since the reminder 804 ≠ 0, we apply division lemma to 302 and 804, to get
804 = 302 x 2 + 200
Step 3: We consider the new divisor 302 and the new remainder 200, and apply the division lemma to get
302 = 200 x 1 + 102
We consider the new divisor 200 and the new remainder 102,and apply the division lemma to get
200 = 102 x 1 + 98
We consider the new divisor 102 and the new remainder 98,and apply the division lemma to get
102 = 98 x 1 + 4
We consider the new divisor 98 and the new remainder 4,and apply the division lemma to get
98 = 4 x 24 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 804 and 2714 is 2
Notice that 2 = HCF(4,2) = HCF(98,4) = HCF(102,98) = HCF(200,102) = HCF(302,200) = HCF(804,302) = HCF(2714,804) .
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Frequently Asked Questions on HCF of 804, 2714 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, 2714?
Answer: HCF of 804, 2714 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 804, 2714 using Euclid's Algorithm?
Answer: For arbitrary numbers 804, 2714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.