Highest Common Factor of 625, 198, 674 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 625, 198, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 625, 198, 674 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 625, 198, 674 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 625, 198, 674 is 1.

HCF(625, 198, 674) = 1

HCF of 625, 198, 674 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 625, 198, 674 is 1.

Highest Common Factor of 625,198,674 using Euclid's algorithm

Highest Common Factor of 625,198,674 is 1

Step 1: Since 625 > 198, we apply the division lemma to 625 and 198, to get

625 = 198 x 3 + 31

Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 31 and 198, to get

198 = 31 x 6 + 12

Step 3: We consider the new divisor 31 and the new remainder 12, and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 625 and 198 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(198,31) = HCF(625,198) .

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

Step 1: Since 674 > 1, we apply the division lemma to 674 and 1, to get

674 = 1 x 674 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 674 is 1

Notice that 1 = HCF(674,1) .

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Frequently Asked Questions on HCF of 625, 198, 674 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 625, 198, 674?

Answer: HCF of 625, 198, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 625, 198, 674 using Euclid's Algorithm?

Answer: For arbitrary numbers 625, 198, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.