Highest Common Factor of 603, 346, 114 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 603, 346, 114 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 603, 346, 114 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 603, 346, 114 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 603, 346, 114 is 1.

HCF(603, 346, 114) = 1

HCF of 603, 346, 114 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 603, 346, 114 is 1.

Highest Common Factor of 603,346,114 using Euclid's algorithm

Highest Common Factor of 603,346,114 is 1

Step 1: Since 603 > 346, we apply the division lemma to 603 and 346, to get

603 = 346 x 1 + 257

Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 257 and 346, to get

346 = 257 x 1 + 89

Step 3: We consider the new divisor 257 and the new remainder 89, and apply the division lemma to get

257 = 89 x 2 + 79

We consider the new divisor 89 and the new remainder 79,and apply the division lemma to get

89 = 79 x 1 + 10

We consider the new divisor 79 and the new remainder 10,and apply the division lemma to get

79 = 10 x 7 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 603 and 346 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(79,10) = HCF(89,79) = HCF(257,89) = HCF(346,257) = HCF(603,346) .

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

Step 1: Since 114 > 1, we apply the division lemma to 114 and 1, to get

114 = 1 x 114 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 114 is 1

Notice that 1 = HCF(114,1) .

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Frequently Asked Questions on HCF of 603, 346, 114 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 603, 346, 114?

Answer: HCF of 603, 346, 114 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 603, 346, 114 using Euclid's Algorithm?

Answer: For arbitrary numbers 603, 346, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.