Highest Common Factor of 504, 921, 718 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 504, 921, 718 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 921, 718 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 504, 921, 718 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 504, 921, 718 is 1.
HCF(504, 921, 718) = 1
HCF of 504, 921, 718 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 921, 718 is 1.
Highest Common Factor of 504,921,718 is 1
Step 1: Since 921 > 504, we apply the division lemma to 921 and 504, to get
921 = 504 x 1 + 417
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 417 and 504, to get
504 = 417 x 1 + 87
Step 3: We consider the new divisor 417 and the new remainder 87, and apply the division lemma to get
417 = 87 x 4 + 69
We consider the new divisor 87 and the new remainder 69,and apply the division lemma to get
87 = 69 x 1 + 18
We consider the new divisor 69 and the new remainder 18,and apply the division lemma to get
69 = 18 x 3 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 504 and 921 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(69,18) = HCF(87,69) = HCF(417,87) = HCF(504,417) = HCF(921,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 718 > 3, we apply the division lemma to 718 and 3, to get
718 = 3 x 239 + 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 718 is 1
Notice that 1 = HCF(3,1) = HCF(718,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 504, 921, 718 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 504, 921, 718?
Answer: HCF of 504, 921, 718 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 921, 718 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 921, 718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.