Highest Common Factor of 873, 501, 178, 243 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 873, 501, 178, 243 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 873, 501, 178, 243 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 873, 501, 178, 243 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 873, 501, 178, 243 is 1.
HCF(873, 501, 178, 243) = 1
HCF of 873, 501, 178, 243 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 873, 501, 178, 243 is 1.
Highest Common Factor of 873,501,178,243 is 1
Step 1: Since 873 > 501, we apply the division lemma to 873 and 501, to get
873 = 501 x 1 + 372
Step 2: Since the reminder 501 ≠ 0, we apply division lemma to 372 and 501, to get
501 = 372 x 1 + 129
Step 3: We consider the new divisor 372 and the new remainder 129, and apply the division lemma to get
372 = 129 x 2 + 114
We consider the new divisor 129 and the new remainder 114,and apply the division lemma to get
129 = 114 x 1 + 15
We consider the new divisor 114 and the new remainder 15,and apply the division lemma to get
114 = 15 x 7 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 873 and 501 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(114,15) = HCF(129,114) = HCF(372,129) = HCF(501,372) = HCF(873,501) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 3, we apply the division lemma to 178 and 3, to get
178 = 3 x 59 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 178 is 1
Notice that 1 = HCF(3,1) = HCF(178,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 243 > 1, we apply the division lemma to 243 and 1, to get
243 = 1 x 243 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 243 is 1
Notice that 1 = HCF(243,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 873, 501, 178, 243 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 873, 501, 178, 243?
Answer: HCF of 873, 501, 178, 243 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 873, 501, 178, 243 using Euclid's Algorithm?
Answer: For arbitrary numbers 873, 501, 178, 243 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.