Highest Common Factor of 830, 106, 321 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 830, 106, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 106, 321 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 830, 106, 321 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 830, 106, 321 is 1.
HCF(830, 106, 321) = 1
HCF of 830, 106, 321 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 830, 106, 321 is 1.
Highest Common Factor of 830,106,321 is 1
Step 1: Since 830 > 106, we apply the division lemma to 830 and 106, to get
830 = 106 x 7 + 88
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 88 and 106, to get
106 = 88 x 1 + 18
Step 3: We consider the new divisor 88 and the new remainder 18, and apply the division lemma to get
88 = 18 x 4 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 830 and 106 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(88,18) = HCF(106,88) = HCF(830,106) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 321 > 2, we apply the division lemma to 321 and 2, to get
321 = 2 x 160 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 321 is 1
Notice that 1 = HCF(2,1) = HCF(321,2) .
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Frequently Asked Questions on HCF of 830, 106, 321 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 830, 106, 321?
Answer: HCF of 830, 106, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 106, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 106, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.