Highest Common Factor of 504, 612, 710, 20 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, 612, 710, 20 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 612, 710, 20 is 2 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, 612, 710, 20 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, 612, 710, 20 is 2.
HCF(504, 612, 710, 20) = 2
HCF of 504, 612, 710, 20 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, 612, 710, 20 is 2.
Highest Common Factor of 504,612,710,20 is 2
Step 1: Since 612 > 504, we apply the division lemma to 612 and 504, to get
612 = 504 x 1 + 108
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 108 and 504, to get
504 = 108 x 4 + 72
Step 3: We consider the new divisor 108 and the new remainder 72, and apply the division lemma to get
108 = 72 x 1 + 36
We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 504 and 612 is 36
Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(504,108) = HCF(612,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 710 > 36, we apply the division lemma to 710 and 36, to get
710 = 36 x 19 + 26
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 26 and 36, to get
36 = 26 x 1 + 10
Step 3: We consider the new divisor 26 and the new remainder 10, and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 36 and 710 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(710,36) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 2, we apply the division lemma to 20 and 2, to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 20 is 2
Notice that 2 = HCF(20,2) .
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Frequently Asked Questions on HCF of 504, 612, 710, 20 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, 612, 710, 20?
Answer: HCF of 504, 612, 710, 20 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 612, 710, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 612, 710, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.