Highest Common Factor of 138, 622, 329 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, 622, 329 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 622, 329 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, 622, 329 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, 622, 329 is 1.
HCF(138, 622, 329) = 1
HCF of 138, 622, 329 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, 622, 329 is 1.
Highest Common Factor of 138,622,329 is 1
Step 1: Since 622 > 138, we apply the division lemma to 622 and 138, to get
622 = 138 x 4 + 70
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 70 and 138, to get
138 = 70 x 1 + 68
Step 3: We consider the new divisor 70 and the new remainder 68, and apply the division lemma to get
70 = 68 x 1 + 2
We consider the new divisor 68 and the new remainder 2, and apply the division lemma to get
68 = 2 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 138 and 622 is 2
Notice that 2 = HCF(68,2) = HCF(70,68) = HCF(138,70) = HCF(622,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 329 > 2, we apply the division lemma to 329 and 2, to get
329 = 2 x 164 + 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 329 is 1
Notice that 1 = HCF(2,1) = HCF(329,2) .
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Frequently Asked Questions on HCF of 138, 622, 329 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, 622, 329?
Answer: HCF of 138, 622, 329 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 622, 329 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 622, 329 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.