Highest Common Factor of 446, 708, 130 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 446, 708, 130 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 446, 708, 130 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 446, 708, 130 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 446, 708, 130 is 2.

HCF(446, 708, 130) = 2

HCF of 446, 708, 130 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 446, 708, 130 is 2.

Highest Common Factor of 446,708,130 using Euclid's algorithm

Highest Common Factor of 446,708,130 is 2

Step 1: Since 708 > 446, we apply the division lemma to 708 and 446, to get

708 = 446 x 1 + 262

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 262 and 446, to get

446 = 262 x 1 + 184

Step 3: We consider the new divisor 262 and the new remainder 184, and apply the division lemma to get

262 = 184 x 1 + 78

We consider the new divisor 184 and the new remainder 78,and apply the division lemma to get

184 = 78 x 2 + 28

We consider the new divisor 78 and the new remainder 28,and apply the division lemma to get

78 = 28 x 2 + 22

We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get

28 = 22 x 1 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 446 and 708 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(78,28) = HCF(184,78) = HCF(262,184) = HCF(446,262) = HCF(708,446) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 130 > 2, we apply the division lemma to 130 and 2, to get

130 = 2 x 65 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 130 is 2

Notice that 2 = HCF(130,2) .

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Frequently Asked Questions on HCF of 446, 708, 130 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 446, 708, 130?

Answer: HCF of 446, 708, 130 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 446, 708, 130 using Euclid's Algorithm?

Answer: For arbitrary numbers 446, 708, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.