Highest Common Factor of 556, 209, 708 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 556, 209, 708 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 556, 209, 708 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 556, 209, 708 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 556, 209, 708 is 1.

HCF(556, 209, 708) = 1

HCF of 556, 209, 708 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 556, 209, 708 is 1.

Highest Common Factor of 556,209,708 using Euclid's algorithm

Highest Common Factor of 556,209,708 is 1

Step 1: Since 556 > 209, we apply the division lemma to 556 and 209, to get

556 = 209 x 2 + 138

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 138 and 209, to get

209 = 138 x 1 + 71

Step 3: We consider the new divisor 138 and the new remainder 71, and apply the division lemma to get

138 = 71 x 1 + 67

We consider the new divisor 71 and the new remainder 67,and apply the division lemma to get

71 = 67 x 1 + 4

We consider the new divisor 67 and the new remainder 4,and apply the division lemma to get

67 = 4 x 16 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 556 and 209 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(67,4) = HCF(71,67) = HCF(138,71) = HCF(209,138) = HCF(556,209) .

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

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

708 = 1 x 708 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 708 is 1

Notice that 1 = HCF(708,1) .

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Frequently Asked Questions on HCF of 556, 209, 708 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 556, 209, 708?

Answer: HCF of 556, 209, 708 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 556, 209, 708 using Euclid's Algorithm?

Answer: For arbitrary numbers 556, 209, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.