Highest Common Factor of 974, 604, 229 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 974, 604, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 604, 229 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 974, 604, 229 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 974, 604, 229 is 1.

HCF(974, 604, 229) = 1

HCF of 974, 604, 229 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 974, 604, 229 is 1.

Highest Common Factor of 974,604,229 using Euclid's algorithm

Highest Common Factor of 974,604,229 is 1

Step 1: Since 974 > 604, we apply the division lemma to 974 and 604, to get

974 = 604 x 1 + 370

Step 2: Since the reminder 604 ≠ 0, we apply division lemma to 370 and 604, to get

604 = 370 x 1 + 234

Step 3: We consider the new divisor 370 and the new remainder 234, and apply the division lemma to get

370 = 234 x 1 + 136

We consider the new divisor 234 and the new remainder 136,and apply the division lemma to get

234 = 136 x 1 + 98

We consider the new divisor 136 and the new remainder 98,and apply the division lemma to get

136 = 98 x 1 + 38

We consider the new divisor 98 and the new remainder 38,and apply the division lemma to get

98 = 38 x 2 + 22

We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get

38 = 22 x 1 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 974 and 604 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(98,38) = HCF(136,98) = HCF(234,136) = HCF(370,234) = HCF(604,370) = HCF(974,604) .

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

Step 1: Since 229 > 2, we apply the division lemma to 229 and 2, to get

229 = 2 x 114 + 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 229 is 1

Notice that 1 = HCF(2,1) = HCF(229,2) .

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Frequently Asked Questions on HCF of 974, 604, 229 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 974, 604, 229?

Answer: HCF of 974, 604, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 604, 229 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 604, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.