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 203, 721, 771 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 203, 721, 771 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 203, 721, 771 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 203, 721, 771 is 1.
HCF(203, 721, 771) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 203, 721, 771 is 1.
Step 1: Since 721 > 203, we apply the division lemma to 721 and 203, to get
721 = 203 x 3 + 112
Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 112 and 203, to get
203 = 112 x 1 + 91
Step 3: We consider the new divisor 112 and the new remainder 91, and apply the division lemma to get
112 = 91 x 1 + 21
We consider the new divisor 91 and the new remainder 21,and apply the division lemma to get
91 = 21 x 4 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 203 and 721 is 7
Notice that 7 = HCF(21,7) = HCF(91,21) = HCF(112,91) = HCF(203,112) = HCF(721,203) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 771 > 7, we apply the division lemma to 771 and 7, to get
771 = 7 x 110 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 771 is 1
Notice that 1 = HCF(7,1) = HCF(771,7) .
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 203, 721, 771?
Answer: HCF of 203, 721, 771 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 203, 721, 771 using Euclid's Algorithm?
Answer: For arbitrary numbers 203, 721, 771 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.