Highest Common Factor of 877, 723 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 877, 723 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 877, 723 is 1 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 877, 723 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 877, 723 is 1.
HCF(877, 723) = 1
HCF of 877, 723 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 877, 723 is 1.
Highest Common Factor of 877,723 is 1
Step 1: Since 877 > 723, we apply the division lemma to 877 and 723, to get
877 = 723 x 1 + 154
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 154 and 723, to get
723 = 154 x 4 + 107
Step 3: We consider the new divisor 154 and the new remainder 107, and apply the division lemma to get
154 = 107 x 1 + 47
We consider the new divisor 107 and the new remainder 47,and apply the division lemma to get
107 = 47 x 2 + 13
We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get
47 = 13 x 3 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 877 and 723 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(107,47) = HCF(154,107) = HCF(723,154) = HCF(877,723) .
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Frequently Asked Questions on HCF of 877, 723 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 877, 723?
Answer: HCF of 877, 723 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 877, 723 using Euclid's Algorithm?
Answer: For arbitrary numbers 877, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
