Highest Common Factor of 877, 1712 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, 1712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 877, 1712 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, 1712 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, 1712 is 1.
HCF(877, 1712) = 1
HCF of 877, 1712 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, 1712 is 1.
Highest Common Factor of 877,1712 is 1
Step 1: Since 1712 > 877, we apply the division lemma to 1712 and 877, to get
1712 = 877 x 1 + 835
Step 2: Since the reminder 877 ≠ 0, we apply division lemma to 835 and 877, to get
877 = 835 x 1 + 42
Step 3: We consider the new divisor 835 and the new remainder 42, and apply the division lemma to get
835 = 42 x 19 + 37
We consider the new divisor 42 and the new remainder 37,and apply the division lemma to get
42 = 37 x 1 + 5
We consider the new divisor 37 and the new remainder 5,and apply the division lemma to get
37 = 5 x 7 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 1712 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(37,5) = HCF(42,37) = HCF(835,42) = HCF(877,835) = HCF(1712,877) .
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Frequently Asked Questions on HCF of 877, 1712 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, 1712?
Answer: HCF of 877, 1712 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 877, 1712 using Euclid's Algorithm?
Answer: For arbitrary numbers 877, 1712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
