Highest Common Factor of 606, 770, 111 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 606, 770, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 606, 770, 111 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 606, 770, 111 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 606, 770, 111 is 1.
HCF(606, 770, 111) = 1
HCF of 606, 770, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 606, 770, 111 is 1.
Highest Common Factor of 606,770,111 is 1
Step 1: Since 770 > 606, we apply the division lemma to 770 and 606, to get
770 = 606 x 1 + 164
Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 164 and 606, to get
606 = 164 x 3 + 114
Step 3: We consider the new divisor 164 and the new remainder 114, and apply the division lemma to get
164 = 114 x 1 + 50
We consider the new divisor 114 and the new remainder 50,and apply the division lemma to get
114 = 50 x 2 + 14
We consider the new divisor 50 and the new remainder 14,and apply the division lemma to get
50 = 14 x 3 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 606 and 770 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(50,14) = HCF(114,50) = HCF(164,114) = HCF(606,164) = HCF(770,606) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 2, we apply the division lemma to 111 and 2, to get
111 = 2 x 55 + 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 111 is 1
Notice that 1 = HCF(2,1) = HCF(111,2) .
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Frequently Asked Questions on HCF of 606, 770, 111 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 606, 770, 111?
Answer: HCF of 606, 770, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 606, 770, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 606, 770, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.