Highest Common Factor of 821, 112, 238, 514 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, 112, 238, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 112, 238, 514 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, 112, 238, 514 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, 112, 238, 514 is 1.
HCF(821, 112, 238, 514) = 1
HCF of 821, 112, 238, 514 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, 112, 238, 514 is 1.
Highest Common Factor of 821,112,238,514 is 1
Step 1: Since 821 > 112, we apply the division lemma to 821 and 112, to get
821 = 112 x 7 + 37
Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 37 and 112, to get
112 = 37 x 3 + 1
Step 3: We consider the new divisor 37 and the new remainder 1, and apply the division lemma to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 112 is 1
Notice that 1 = HCF(37,1) = HCF(112,37) = HCF(821,112) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 238 > 1, we apply the division lemma to 238 and 1, to get
238 = 1 x 238 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 238 is 1
Notice that 1 = HCF(238,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get
514 = 1 x 514 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1
Notice that 1 = HCF(514,1) .
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Frequently Asked Questions on HCF of 821, 112, 238, 514 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, 112, 238, 514?
Answer: HCF of 821, 112, 238, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 112, 238, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 112, 238, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.