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 348, 422, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 348, 422, 129 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 348, 422, 129 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 348, 422, 129 is 1.
HCF(348, 422, 129) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 348, 422, 129 is 1.
Step 1: Since 422 > 348, we apply the division lemma to 422 and 348, to get
422 = 348 x 1 + 74
Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 74 and 348, to get
348 = 74 x 4 + 52
Step 3: We consider the new divisor 74 and the new remainder 52, and apply the division lemma to get
74 = 52 x 1 + 22
We consider the new divisor 52 and the new remainder 22,and apply the division lemma to get
52 = 22 x 2 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 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 348 and 422 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(52,22) = HCF(74,52) = HCF(348,74) = HCF(422,348) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 2, we apply the division lemma to 129 and 2, to get
129 = 2 x 64 + 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 129 is 1
Notice that 1 = HCF(2,1) = HCF(129,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 348, 422, 129?
Answer: HCF of 348, 422, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 348, 422, 129 using Euclid's Algorithm?
Answer: For arbitrary numbers 348, 422, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.