Highest Common Factor of 355, 972, 208 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 355, 972, 208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 355, 972, 208 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 355, 972, 208 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 355, 972, 208 is 1.

HCF(355, 972, 208) = 1

HCF of 355, 972, 208 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 355, 972, 208 is 1.

Highest Common Factor of 355,972,208 using Euclid's algorithm

Highest Common Factor of 355,972,208 is 1

Step 1: Since 972 > 355, we apply the division lemma to 972 and 355, to get

972 = 355 x 2 + 262

Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 262 and 355, to get

355 = 262 x 1 + 93

Step 3: We consider the new divisor 262 and the new remainder 93, and apply the division lemma to get

262 = 93 x 2 + 76

We consider the new divisor 93 and the new remainder 76,and apply the division lemma to get

93 = 76 x 1 + 17

We consider the new divisor 76 and the new remainder 17,and apply the division lemma to get

76 = 17 x 4 + 8

We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get

17 = 8 x 2 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 355 and 972 is 1

Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(76,17) = HCF(93,76) = HCF(262,93) = HCF(355,262) = HCF(972,355) .

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

Step 1: Since 208 > 1, we apply the division lemma to 208 and 1, to get

208 = 1 x 208 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 208 is 1

Notice that 1 = HCF(208,1) .

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Frequently Asked Questions on HCF of 355, 972, 208 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 355, 972, 208?

Answer: HCF of 355, 972, 208 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 355, 972, 208 using Euclid's Algorithm?

Answer: For arbitrary numbers 355, 972, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.