Highest Common Factor of 602, 914, 57 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 602, 914, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 602, 914, 57 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 602, 914, 57 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 602, 914, 57 is 1.

HCF(602, 914, 57) = 1

HCF of 602, 914, 57 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 602, 914, 57 is 1.

Highest Common Factor of 602,914,57 using Euclid's algorithm

Highest Common Factor of 602,914,57 is 1

Step 1: Since 914 > 602, we apply the division lemma to 914 and 602, to get

914 = 602 x 1 + 312

Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 312 and 602, to get

602 = 312 x 1 + 290

Step 3: We consider the new divisor 312 and the new remainder 290, and apply the division lemma to get

312 = 290 x 1 + 22

We consider the new divisor 290 and the new remainder 22,and apply the division lemma to get

290 = 22 x 13 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 602 and 914 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(290,22) = HCF(312,290) = HCF(602,312) = HCF(914,602) .

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

Step 1: Since 57 > 2, we apply the division lemma to 57 and 2, to get

57 = 2 x 28 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 57 is 1

Notice that 1 = HCF(2,1) = HCF(57,2) .

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Frequently Asked Questions on HCF of 602, 914, 57 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 602, 914, 57?

Answer: HCF of 602, 914, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 602, 914, 57 using Euclid's Algorithm?

Answer: For arbitrary numbers 602, 914, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.