Highest Common Factor of 123, 772, 80 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 123, 772, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 123, 772, 80 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 123, 772, 80 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 123, 772, 80 is 1.
HCF(123, 772, 80) = 1
HCF of 123, 772, 80 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 123, 772, 80 is 1.
Highest Common Factor of 123,772,80 is 1
Step 1: Since 772 > 123, we apply the division lemma to 772 and 123, to get
772 = 123 x 6 + 34
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 34 and 123, to get
123 = 34 x 3 + 21
Step 3: We consider the new divisor 34 and the new remainder 21, and apply the division lemma to get
34 = 21 x 1 + 13
We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get
21 = 13 x 1 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 123 and 772 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(123,34) = HCF(772,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get
80 = 1 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1
Notice that 1 = HCF(80,1) .
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Frequently Asked Questions on HCF of 123, 772, 80 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 123, 772, 80?
Answer: HCF of 123, 772, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 123, 772, 80 using Euclid's Algorithm?
Answer: For arbitrary numbers 123, 772, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.