Highest Common Factor of 819, 504, 120 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 819, 504, 120 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 819, 504, 120 is 3 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 819, 504, 120 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 819, 504, 120 is 3.
HCF(819, 504, 120) = 3
HCF of 819, 504, 120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 819, 504, 120 is 3.
Highest Common Factor of 819,504,120 is 3
Step 1: Since 819 > 504, we apply the division lemma to 819 and 504, to get
819 = 504 x 1 + 315
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 315 and 504, to get
504 = 315 x 1 + 189
Step 3: We consider the new divisor 315 and the new remainder 189, and apply the division lemma to get
315 = 189 x 1 + 126
We consider the new divisor 189 and the new remainder 126,and apply the division lemma to get
189 = 126 x 1 + 63
We consider the new divisor 126 and the new remainder 63,and apply the division lemma to get
126 = 63 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 63, the HCF of 819 and 504 is 63
Notice that 63 = HCF(126,63) = HCF(189,126) = HCF(315,189) = HCF(504,315) = HCF(819,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 63, we apply the division lemma to 120 and 63, to get
120 = 63 x 1 + 57
Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 57 and 63, to get
63 = 57 x 1 + 6
Step 3: We consider the new divisor 57 and the new remainder 6, and apply the division lemma to get
57 = 6 x 9 + 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 63 and 120 is 3
Notice that 3 = HCF(6,3) = HCF(57,6) = HCF(63,57) = HCF(120,63) .
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Frequently Asked Questions on HCF of 819, 504, 120 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 819, 504, 120?
Answer: HCF of 819, 504, 120 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 819, 504, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 819, 504, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.