Highest Common Factor of 197, 932, 774 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 197, 932, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 197, 932, 774 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 197, 932, 774 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 197, 932, 774 is 1.

HCF(197, 932, 774) = 1

HCF of 197, 932, 774 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 197, 932, 774 is 1.

Highest Common Factor of 197,932,774 using Euclid's algorithm

Highest Common Factor of 197,932,774 is 1

Step 1: Since 932 > 197, we apply the division lemma to 932 and 197, to get

932 = 197 x 4 + 144

Step 2: Since the reminder 197 ≠ 0, we apply division lemma to 144 and 197, to get

197 = 144 x 1 + 53

Step 3: We consider the new divisor 144 and the new remainder 53, and apply the division lemma to get

144 = 53 x 2 + 38

We consider the new divisor 53 and the new remainder 38,and apply the division lemma to get

53 = 38 x 1 + 15

We consider the new divisor 38 and the new remainder 15,and apply the division lemma to get

38 = 15 x 2 + 8

We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get

15 = 8 x 1 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 197 and 932 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(38,15) = HCF(53,38) = HCF(144,53) = HCF(197,144) = HCF(932,197) .

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

Step 1: Since 774 > 1, we apply the division lemma to 774 and 1, to get

774 = 1 x 774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 774 is 1

Notice that 1 = HCF(774,1) .

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Frequently Asked Questions on HCF of 197, 932, 774 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 197, 932, 774?

Answer: HCF of 197, 932, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 197, 932, 774 using Euclid's Algorithm?

Answer: For arbitrary numbers 197, 932, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.