Highest Common Factor of 504, 420, 805 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, 420, 805 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 420, 805 is 7 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, 420, 805 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, 420, 805 is 7.
HCF(504, 420, 805) = 7
HCF of 504, 420, 805 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, 420, 805 is 7.
Highest Common Factor of 504,420,805 is 7
Step 1: Since 504 > 420, we apply the division lemma to 504 and 420, to get
504 = 420 x 1 + 84
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 84 and 420, to get
420 = 84 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 84, the HCF of 504 and 420 is 84
Notice that 84 = HCF(420,84) = HCF(504,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 805 > 84, we apply the division lemma to 805 and 84, to get
805 = 84 x 9 + 49
Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 49 and 84, to get
84 = 49 x 1 + 35
Step 3: We consider the new divisor 49 and the new remainder 35, and apply the division lemma to get
49 = 35 x 1 + 14
We consider the new divisor 35 and the new remainder 14,and apply the division lemma to get
35 = 14 x 2 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 84 and 805 is 7
Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(49,35) = HCF(84,49) = HCF(805,84) .
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, 420, 805 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, 420, 805?
Answer: HCF of 504, 420, 805 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 420, 805 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 420, 805 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.