Highest Common Factor of 320, 529, 109 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 320, 529, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 529, 109 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 320, 529, 109 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 320, 529, 109 is 1.
HCF(320, 529, 109) = 1
HCF of 320, 529, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 529, 109 is 1.
Highest Common Factor of 320,529,109 is 1
Step 1: Since 529 > 320, we apply the division lemma to 529 and 320, to get
529 = 320 x 1 + 209
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 209 and 320, to get
320 = 209 x 1 + 111
Step 3: We consider the new divisor 209 and the new remainder 111, and apply the division lemma to get
209 = 111 x 1 + 98
We consider the new divisor 111 and the new remainder 98,and apply the division lemma to get
111 = 98 x 1 + 13
We consider the new divisor 98 and the new remainder 13,and apply the division lemma to get
98 = 13 x 7 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 320 and 529 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(98,13) = HCF(111,98) = HCF(209,111) = HCF(320,209) = HCF(529,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
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Frequently Asked Questions on HCF of 320, 529, 109 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 320, 529, 109?
Answer: HCF of 320, 529, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 529, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 529, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.