Highest Common Factor of 420, 225, 734 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 420, 225, 734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 225, 734 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 420, 225, 734 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 420, 225, 734 is 1.

HCF(420, 225, 734) = 1

HCF of 420, 225, 734 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 420, 225, 734 is 1.

Highest Common Factor of 420,225,734 using Euclid's algorithm

Highest Common Factor of 420,225,734 is 1

Step 1: Since 420 > 225, we apply the division lemma to 420 and 225, to get

420 = 225 x 1 + 195

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 195 and 225, to get

225 = 195 x 1 + 30

Step 3: We consider the new divisor 195 and the new remainder 30, and apply the division lemma to get

195 = 30 x 6 + 15

We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 420 and 225 is 15

Notice that 15 = HCF(30,15) = HCF(195,30) = HCF(225,195) = HCF(420,225) .

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

Step 1: Since 734 > 15, we apply the division lemma to 734 and 15, to get

734 = 15 x 48 + 14

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 14 and 15, to get

15 = 14 x 1 + 1

Step 3: We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 734 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(734,15) .

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Frequently Asked Questions on HCF of 420, 225, 734 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 420, 225, 734?

Answer: HCF of 420, 225, 734 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 225, 734 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 225, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.