Highest Common Factor of 864, 1724 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 864, 1724 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 1724 is 4 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 864, 1724 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 864, 1724 is 4.
HCF(864, 1724) = 4
HCF of 864, 1724 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 1724 is 4.
Highest Common Factor of 864,1724 is 4
Step 1: Since 1724 > 864, we apply the division lemma to 1724 and 864, to get
1724 = 864 x 1 + 860
Step 2: Since the reminder 864 ≠ 0, we apply division lemma to 860 and 864, to get
864 = 860 x 1 + 4
Step 3: We consider the new divisor 860 and the new remainder 4, and apply the division lemma to get
860 = 4 x 215 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 864 and 1724 is 4
Notice that 4 = HCF(860,4) = HCF(864,860) = HCF(1724,864) .
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Frequently Asked Questions on HCF of 864, 1724 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 864, 1724?
Answer: HCF of 864, 1724 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 1724 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 1724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.