Highest Common Factor of 504, 372, 106 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, 372, 106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 372, 106 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, 372, 106 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, 372, 106 is 2.
HCF(504, 372, 106) = 2
HCF of 504, 372, 106 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, 372, 106 is 2.
Highest Common Factor of 504,372,106 is 2
Step 1: Since 504 > 372, we apply the division lemma to 504 and 372, to get
504 = 372 x 1 + 132
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 132 and 372, to get
372 = 132 x 2 + 108
Step 3: We consider the new divisor 132 and the new remainder 108, and apply the division lemma to get
132 = 108 x 1 + 24
We consider the new divisor 108 and the new remainder 24,and apply the division lemma to get
108 = 24 x 4 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 504 and 372 is 12
Notice that 12 = HCF(24,12) = HCF(108,24) = HCF(132,108) = HCF(372,132) = HCF(504,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 12, we apply the division lemma to 106 and 12, to get
106 = 12 x 8 + 10
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 10 and 12, to get
12 = 10 x 1 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 106 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(106,12) .
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Frequently Asked Questions on HCF of 504, 372, 106 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, 372, 106?
Answer: HCF of 504, 372, 106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 372, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 372, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.