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 31, 32, 314, 206 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 31, 32, 314, 206 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 31, 32, 314, 206 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 31, 32, 314, 206 is 1.
HCF(31, 32, 314, 206) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 31, 32, 314, 206 is 1.
Step 1: Since 32 > 31, we apply the division lemma to 32 and 31, to get
32 = 31 x 1 + 1
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 1 and 31, to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 32 is 1
Notice that 1 = HCF(31,1) = HCF(32,31) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 1, we apply the division lemma to 314 and 1, to get
314 = 1 x 314 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 314 is 1
Notice that 1 = HCF(314,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 206 > 1, we apply the division lemma to 206 and 1, to get
206 = 1 x 206 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 206 is 1
Notice that 1 = HCF(206,1) .
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 31, 32, 314, 206?
Answer: HCF of 31, 32, 314, 206 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 31, 32, 314, 206 using Euclid's Algorithm?
Answer: For arbitrary numbers 31, 32, 314, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.