Highest Common Factor of 821, 509, 56 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 821, 509, 56 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 509, 56 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 821, 509, 56 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 821, 509, 56 is 1.
HCF(821, 509, 56) = 1
HCF of 821, 509, 56 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 509, 56 is 1.
Highest Common Factor of 821,509,56 is 1
Step 1: Since 821 > 509, we apply the division lemma to 821 and 509, to get
821 = 509 x 1 + 312
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 312 and 509, to get
509 = 312 x 1 + 197
Step 3: We consider the new divisor 312 and the new remainder 197, and apply the division lemma to get
312 = 197 x 1 + 115
We consider the new divisor 197 and the new remainder 115,and apply the division lemma to get
197 = 115 x 1 + 82
We consider the new divisor 115 and the new remainder 82,and apply the division lemma to get
115 = 82 x 1 + 33
We consider the new divisor 82 and the new remainder 33,and apply the division lemma to get
82 = 33 x 2 + 16
We consider the new divisor 33 and the new remainder 16,and apply the division lemma to get
33 = 16 x 2 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 509 is 1
Notice that 1 = HCF(16,1) = HCF(33,16) = HCF(82,33) = HCF(115,82) = HCF(197,115) = HCF(312,197) = HCF(509,312) = HCF(821,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 56 > 1, we apply the division lemma to 56 and 1, to get
56 = 1 x 56 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 56 is 1
Notice that 1 = HCF(56,1) .
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Frequently Asked Questions on HCF of 821, 509, 56 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 821, 509, 56?
Answer: HCF of 821, 509, 56 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 509, 56 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 509, 56 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.