Highest Common Factor of 878, 509 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 878, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 878, 509 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 878, 509 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 878, 509 is 1.
HCF(878, 509) = 1
HCF of 878, 509 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 878, 509 is 1.
Highest Common Factor of 878,509 is 1
Step 1: Since 878 > 509, we apply the division lemma to 878 and 509, to get
878 = 509 x 1 + 369
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 369 and 509, to get
509 = 369 x 1 + 140
Step 3: We consider the new divisor 369 and the new remainder 140, and apply the division lemma to get
369 = 140 x 2 + 89
We consider the new divisor 140 and the new remainder 89,and apply the division lemma to get
140 = 89 x 1 + 51
We consider the new divisor 89 and the new remainder 51,and apply the division lemma to get
89 = 51 x 1 + 38
We consider the new divisor 51 and the new remainder 38,and apply the division lemma to get
51 = 38 x 1 + 13
We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get
38 = 13 x 2 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 878 and 509 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(51,38) = HCF(89,51) = HCF(140,89) = HCF(369,140) = HCF(509,369) = HCF(878,509) .
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Frequently Asked Questions on HCF of 878, 509 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 878, 509?
Answer: HCF of 878, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 878, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 878, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.