Highest Common Factor of 660, 463, 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 660, 463, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 463, 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 660, 463, 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 660, 463, 109 is 1.
HCF(660, 463, 109) = 1
HCF of 660, 463, 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 660, 463, 109 is 1.
Highest Common Factor of 660,463,109 is 1
Step 1: Since 660 > 463, we apply the division lemma to 660 and 463, to get
660 = 463 x 1 + 197
Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 197 and 463, to get
463 = 197 x 2 + 69
Step 3: We consider the new divisor 197 and the new remainder 69, and apply the division lemma to get
197 = 69 x 2 + 59
We consider the new divisor 69 and the new remainder 59,and apply the division lemma to get
69 = 59 x 1 + 10
We consider the new divisor 59 and the new remainder 10,and apply the division lemma to get
59 = 10 x 5 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 660 and 463 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(59,10) = HCF(69,59) = HCF(197,69) = HCF(463,197) = HCF(660,463) .
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 660, 463, 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 660, 463, 109?
Answer: HCF of 660, 463, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 463, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 463, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.