Highest Common Factor of 504, 192, 131, 19 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, 192, 131, 19 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 192, 131, 19 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, 192, 131, 19 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, 192, 131, 19 is 1.
HCF(504, 192, 131, 19) = 1
HCF of 504, 192, 131, 19 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, 192, 131, 19 is 1.
Highest Common Factor of 504,192,131,19 is 1
Step 1: Since 504 > 192, we apply the division lemma to 504 and 192, to get
504 = 192 x 2 + 120
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 120 and 192, to get
192 = 120 x 1 + 72
Step 3: We consider the new divisor 120 and the new remainder 72, and apply the division lemma to get
120 = 72 x 1 + 48
We consider the new divisor 72 and the new remainder 48,and apply the division lemma to get
72 = 48 x 1 + 24
We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 504 and 192 is 24
Notice that 24 = HCF(48,24) = HCF(72,48) = HCF(120,72) = HCF(192,120) = HCF(504,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 131 > 24, we apply the division lemma to 131 and 24, to get
131 = 24 x 5 + 11
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 11 and 24, to get
24 = 11 x 2 + 2
Step 3: We consider the new divisor 11 and the new remainder 2, and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 24 and 131 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(131,24) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 19 > 1, we apply the division lemma to 19 and 1, to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 19 is 1
Notice that 1 = HCF(19,1) .
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Frequently Asked Questions on HCF of 504, 192, 131, 19 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, 192, 131, 19?
Answer: HCF of 504, 192, 131, 19 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 192, 131, 19 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 192, 131, 19 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.