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, 228, 331 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 348, 228, 331 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, 228, 331 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, 228, 331 is 1.
HCF(348, 228, 331) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 348, 228, 331 is 1.
Step 1: Since 348 > 228, we apply the division lemma to 348 and 228, to get
348 = 228 x 1 + 120
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 120 and 228, to get
228 = 120 x 1 + 108
Step 3: We consider the new divisor 120 and the new remainder 108, and apply the division lemma to get
120 = 108 x 1 + 12
We consider the new divisor 108 and the new remainder 12, and apply the division lemma to get
108 = 12 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 348 and 228 is 12
Notice that 12 = HCF(108,12) = HCF(120,108) = HCF(228,120) = HCF(348,228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 331 > 12, we apply the division lemma to 331 and 12, to get
331 = 12 x 27 + 7
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 7 and 12, to get
12 = 7 x 1 + 5
Step 3: We consider the new divisor 7 and the new remainder 5, and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 12 and 331 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(331,12) .
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, 228, 331?
Answer: HCF of 348, 228, 331 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 348, 228, 331 using Euclid's Algorithm?
Answer: For arbitrary numbers 348, 228, 331 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.