Highest Common Factor of 420, 308, 506 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 420, 308, 506 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 308, 506 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 420, 308, 506 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 420, 308, 506 is 2.
HCF(420, 308, 506) = 2
HCF of 420, 308, 506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 308, 506 is 2.
Highest Common Factor of 420,308,506 is 2
Step 1: Since 420 > 308, we apply the division lemma to 420 and 308, to get
420 = 308 x 1 + 112
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 112 and 308, to get
308 = 112 x 2 + 84
Step 3: We consider the new divisor 112 and the new remainder 84, and apply the division lemma to get
112 = 84 x 1 + 28
We consider the new divisor 84 and the new remainder 28, and apply the division lemma to get
84 = 28 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 420 and 308 is 28
Notice that 28 = HCF(84,28) = HCF(112,84) = HCF(308,112) = HCF(420,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 506 > 28, we apply the division lemma to 506 and 28, to get
506 = 28 x 18 + 2
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 2 and 28, to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 28 and 506 is 2
Notice that 2 = HCF(28,2) = HCF(506,28) .
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Frequently Asked Questions on HCF of 420, 308, 506 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 420, 308, 506?
Answer: HCF of 420, 308, 506 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 308, 506 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 308, 506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.