Highest Common Factor of 827, 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 827, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 827, 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 827, 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 827, 509 is 1.
HCF(827, 509) = 1
HCF of 827, 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 827, 509 is 1.
Highest Common Factor of 827,509 is 1
Step 1: Since 827 > 509, we apply the division lemma to 827 and 509, to get
827 = 509 x 1 + 318
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 318 and 509, to get
509 = 318 x 1 + 191
Step 3: We consider the new divisor 318 and the new remainder 191, and apply the division lemma to get
318 = 191 x 1 + 127
We consider the new divisor 191 and the new remainder 127,and apply the division lemma to get
191 = 127 x 1 + 64
We consider the new divisor 127 and the new remainder 64,and apply the division lemma to get
127 = 64 x 1 + 63
We consider the new divisor 64 and the new remainder 63,and apply the division lemma to get
64 = 63 x 1 + 1
We consider the new divisor 63 and the new remainder 1,and apply the division lemma to get
63 = 1 x 63 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 827 and 509 is 1
Notice that 1 = HCF(63,1) = HCF(64,63) = HCF(127,64) = HCF(191,127) = HCF(318,191) = HCF(509,318) = HCF(827,509) .
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Frequently Asked Questions on HCF of 827, 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 827, 509?
Answer: HCF of 827, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 827, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 827, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.