Highest Common Factor of 506, 872, 168 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 506, 872, 168 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 872, 168 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 506, 872, 168 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 506, 872, 168 is 2.
HCF(506, 872, 168) = 2
HCF of 506, 872, 168 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 872, 168 is 2.
Highest Common Factor of 506,872,168 is 2
Step 1: Since 872 > 506, we apply the division lemma to 872 and 506, to get
872 = 506 x 1 + 366
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 366 and 506, to get
506 = 366 x 1 + 140
Step 3: We consider the new divisor 366 and the new remainder 140, and apply the division lemma to get
366 = 140 x 2 + 86
We consider the new divisor 140 and the new remainder 86,and apply the division lemma to get
140 = 86 x 1 + 54
We consider the new divisor 86 and the new remainder 54,and apply the division lemma to get
86 = 54 x 1 + 32
We consider the new divisor 54 and the new remainder 32,and apply the division lemma to get
54 = 32 x 1 + 22
We consider the new divisor 32 and the new remainder 22,and apply the division lemma to get
32 = 22 x 1 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
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 506 and 872 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(54,32) = HCF(86,54) = HCF(140,86) = HCF(366,140) = HCF(506,366) = HCF(872,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 168 > 2, we apply the division lemma to 168 and 2, to get
168 = 2 x 84 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 168 is 2
Notice that 2 = HCF(168,2) .
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Frequently Asked Questions on HCF of 506, 872, 168 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 506, 872, 168?
Answer: HCF of 506, 872, 168 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 872, 168 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 872, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.