Highest Common Factor of 721, 998, 800, 51 using Euclid's algorithm
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 721, 998, 800, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 998, 800, 51 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 721, 998, 800, 51 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 721, 998, 800, 51 is 1.
HCF(721, 998, 800, 51) = 1
HCF of 721, 998, 800, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 998, 800, 51 is 1.
Highest Common Factor of 721,998,800,51 is 1
Step 1: Since 998 > 721, we apply the division lemma to 998 and 721, to get
998 = 721 x 1 + 277
Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 277 and 721, to get
721 = 277 x 2 + 167
Step 3: We consider the new divisor 277 and the new remainder 167, and apply the division lemma to get
277 = 167 x 1 + 110
We consider the new divisor 167 and the new remainder 110,and apply the division lemma to get
167 = 110 x 1 + 57
We consider the new divisor 110 and the new remainder 57,and apply the division lemma to get
110 = 57 x 1 + 53
We consider the new divisor 57 and the new remainder 53,and apply the division lemma to get
57 = 53 x 1 + 4
We consider the new divisor 53 and the new remainder 4,and apply the division lemma to get
53 = 4 x 13 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 721 and 998 is 1
Notice that 1 = HCF(4,1) = HCF(53,4) = HCF(57,53) = HCF(110,57) = HCF(167,110) = HCF(277,167) = HCF(721,277) = HCF(998,721) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 800 > 1, we apply the division lemma to 800 and 1, to get
800 = 1 x 800 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 800 is 1
Notice that 1 = HCF(800,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1
Notice that 1 = HCF(51,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 721, 998, 800, 51 using Euclid's Algorithm
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 721, 998, 800, 51?
Answer: HCF of 721, 998, 800, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 998, 800, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 998, 800, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.