Highest Common Factor of 402, 245, 35 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 402, 245, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 402, 245, 35 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 402, 245, 35 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 402, 245, 35 is 1.

HCF(402, 245, 35) = 1

HCF of 402, 245, 35 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 402, 245, 35 is 1.

Highest Common Factor of 402,245,35 using Euclid's algorithm

Highest Common Factor of 402,245,35 is 1

Step 1: Since 402 > 245, we apply the division lemma to 402 and 245, to get

402 = 245 x 1 + 157

Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 157 and 245, to get

245 = 157 x 1 + 88

Step 3: We consider the new divisor 157 and the new remainder 88, and apply the division lemma to get

157 = 88 x 1 + 69

We consider the new divisor 88 and the new remainder 69,and apply the division lemma to get

88 = 69 x 1 + 19

We consider the new divisor 69 and the new remainder 19,and apply the division lemma to get

69 = 19 x 3 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 402 and 245 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(69,19) = HCF(88,69) = HCF(157,88) = HCF(245,157) = HCF(402,245) .

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

Step 1: Since 35 > 1, we apply the division lemma to 35 and 1, to get

35 = 1 x 35 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 35 is 1

Notice that 1 = HCF(35,1) .

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Frequently Asked Questions on HCF of 402, 245, 35 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 402, 245, 35?

Answer: HCF of 402, 245, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 402, 245, 35 using Euclid's Algorithm?

Answer: For arbitrary numbers 402, 245, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.