Highest Common Factor of 138, 777, 697 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 138, 777, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 777, 697 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 138, 777, 697 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 138, 777, 697 is 1.
HCF(138, 777, 697) = 1
HCF of 138, 777, 697 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 777, 697 is 1.
Highest Common Factor of 138,777,697 is 1
Step 1: Since 777 > 138, we apply the division lemma to 777 and 138, to get
777 = 138 x 5 + 87
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 87 and 138, to get
138 = 87 x 1 + 51
Step 3: We consider the new divisor 87 and the new remainder 51, and apply the division lemma to get
87 = 51 x 1 + 36
We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get
51 = 36 x 1 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 138 and 777 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(138,87) = HCF(777,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 697 > 3, we apply the division lemma to 697 and 3, to get
697 = 3 x 232 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 697 is 1
Notice that 1 = HCF(3,1) = HCF(697,3) .
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Frequently Asked Questions on HCF of 138, 777, 697 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 138, 777, 697?
Answer: HCF of 138, 777, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 777, 697 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 777, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.