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 339, 396, 214, 980 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 339, 396, 214, 980 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 339, 396, 214, 980 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 339, 396, 214, 980 is 1.
HCF(339, 396, 214, 980) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 339, 396, 214, 980 is 1.
Step 1: Since 396 > 339, we apply the division lemma to 396 and 339, to get
396 = 339 x 1 + 57
Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 57 and 339, to get
339 = 57 x 5 + 54
Step 3: We consider the new divisor 57 and the new remainder 54, and apply the division lemma to get
57 = 54 x 1 + 3
We consider the new divisor 54 and the new remainder 3, and apply the division lemma to get
54 = 3 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 339 and 396 is 3
Notice that 3 = HCF(54,3) = HCF(57,54) = HCF(339,57) = HCF(396,339) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 214 > 3, we apply the division lemma to 214 and 3, to get
214 = 3 x 71 + 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 214 is 1
Notice that 1 = HCF(3,1) = HCF(214,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 980 > 1, we apply the division lemma to 980 and 1, to get
980 = 1 x 980 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 980 is 1
Notice that 1 = HCF(980,1) .
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 339, 396, 214, 980?
Answer: HCF of 339, 396, 214, 980 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 339, 396, 214, 980 using Euclid's Algorithm?
Answer: For arbitrary numbers 339, 396, 214, 980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.