Highest Common Factor of 974, 698, 177 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, 698, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 698, 177 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, 698, 177 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, 698, 177 is 1.

HCF(974, 698, 177) = 1

HCF of 974, 698, 177 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, 698, 177 is 1.

Highest Common Factor of 974,698,177 using Euclid's algorithm

Highest Common Factor of 974,698,177 is 1

Step 1: Since 974 > 698, we apply the division lemma to 974 and 698, to get

974 = 698 x 1 + 276

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 276 and 698, to get

698 = 276 x 2 + 146

Step 3: We consider the new divisor 276 and the new remainder 146, and apply the division lemma to get

276 = 146 x 1 + 130

We consider the new divisor 146 and the new remainder 130,and apply the division lemma to get

146 = 130 x 1 + 16

We consider the new divisor 130 and the new remainder 16,and apply the division lemma to get

130 = 16 x 8 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 698 is 2

Notice that 2 = HCF(16,2) = HCF(130,16) = HCF(146,130) = HCF(276,146) = HCF(698,276) = HCF(974,698) .

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

Step 1: Since 177 > 2, we apply the division lemma to 177 and 2, to get

177 = 2 x 88 + 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 177 is 1

Notice that 1 = HCF(2,1) = HCF(177,2) .

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Frequently Asked Questions on HCF of 974, 698, 177 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, 698, 177?

Answer: HCF of 974, 698, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 698, 177 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 698, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.