Highest Common Factor of 945, 360, 452 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 945, 360, 452 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 945, 360, 452 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 945, 360, 452 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 945, 360, 452 is 1.

HCF(945, 360, 452) = 1

HCF of 945, 360, 452 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 945, 360, 452 is 1.

Highest Common Factor of 945,360,452 using Euclid's algorithm

Highest Common Factor of 945,360,452 is 1

Step 1: Since 945 > 360, we apply the division lemma to 945 and 360, to get

945 = 360 x 2 + 225

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 225 and 360, to get

360 = 225 x 1 + 135

Step 3: We consider the new divisor 225 and the new remainder 135, and apply the division lemma to get

225 = 135 x 1 + 90

We consider the new divisor 135 and the new remainder 90,and apply the division lemma to get

135 = 90 x 1 + 45

We consider the new divisor 90 and the new remainder 45,and apply the division lemma to get

90 = 45 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 945 and 360 is 45

Notice that 45 = HCF(90,45) = HCF(135,90) = HCF(225,135) = HCF(360,225) = HCF(945,360) .

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

Step 1: Since 452 > 45, we apply the division lemma to 452 and 45, to get

452 = 45 x 10 + 2

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 2 and 45, to get

45 = 2 x 22 + 1

Step 3: 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 45 and 452 is 1

Notice that 1 = HCF(2,1) = HCF(45,2) = HCF(452,45) .

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Frequently Asked Questions on HCF of 945, 360, 452 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 945, 360, 452?

Answer: HCF of 945, 360, 452 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 945, 360, 452 using Euclid's Algorithm?

Answer: For arbitrary numbers 945, 360, 452 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.