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 270, 474, 14, 671 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 474, 14, 671 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 270, 474, 14, 671 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 270, 474, 14, 671 is 1.
HCF(270, 474, 14, 671) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 474, 14, 671 is 1.
Step 1: Since 474 > 270, we apply the division lemma to 474 and 270, to get
474 = 270 x 1 + 204
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 204 and 270, to get
270 = 204 x 1 + 66
Step 3: We consider the new divisor 204 and the new remainder 66, and apply the division lemma to get
204 = 66 x 3 + 6
We consider the new divisor 66 and the new remainder 6, and apply the division lemma to get
66 = 6 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 270 and 474 is 6
Notice that 6 = HCF(66,6) = HCF(204,66) = HCF(270,204) = HCF(474,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 6, we apply the division lemma to 14 and 6, to get
14 = 6 x 2 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 14 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 671 > 2, we apply the division lemma to 671 and 2, to get
671 = 2 x 335 + 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 671 is 1
Notice that 1 = HCF(2,1) = HCF(671,2) .
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 270, 474, 14, 671?
Answer: HCF of 270, 474, 14, 671 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 474, 14, 671 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 474, 14, 671 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.