Highest Common Factor of 360, 615, 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 360, 615, 734 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 615, 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 360, 615, 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 360, 615, 734 is 1.

HCF(360, 615, 734) = 1

HCF of 360, 615, 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 360, 615, 734 is 1.

Highest Common Factor of 360,615,734 using Euclid's algorithm

Highest Common Factor of 360,615,734 is 1

Step 1: Since 615 > 360, we apply the division lemma to 615 and 360, to get

615 = 360 x 1 + 255

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 255 and 360, to get

360 = 255 x 1 + 105

Step 3: We consider the new divisor 255 and the new remainder 105, and apply the division lemma to get

255 = 105 x 2 + 45

We consider the new divisor 105 and the new remainder 45,and apply the division lemma to get

105 = 45 x 2 + 15

We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get

45 = 15 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 360 and 615 is 15

Notice that 15 = HCF(45,15) = HCF(105,45) = HCF(255,105) = HCF(360,255) = HCF(615,360) .

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 360, 615, 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 360, 615, 734?

Answer: HCF of 360, 615, 734 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 615, 734 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 615, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.