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 455, 320, 311 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 320, 311 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 455, 320, 311 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 455, 320, 311 is 1.
HCF(455, 320, 311) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 320, 311 is 1.
Step 1: Since 455 > 320, we apply the division lemma to 455 and 320, to get
455 = 320 x 1 + 135
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 135 and 320, to get
320 = 135 x 2 + 50
Step 3: We consider the new divisor 135 and the new remainder 50, and apply the division lemma to get
135 = 50 x 2 + 35
We consider the new divisor 50 and the new remainder 35,and apply the division lemma to get
50 = 35 x 1 + 15
We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 455 and 320 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(50,35) = HCF(135,50) = HCF(320,135) = HCF(455,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 311 > 5, we apply the division lemma to 311 and 5, to get
311 = 5 x 62 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 311 is 1
Notice that 1 = HCF(5,1) = HCF(311,5) .
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 455, 320, 311?
Answer: HCF of 455, 320, 311 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 320, 311 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 320, 311 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.