Highest Common Factor of 945, 506, 612 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, 506, 612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 945, 506, 612 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, 506, 612 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, 506, 612 is 1.

HCF(945, 506, 612) = 1

HCF of 945, 506, 612 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, 506, 612 is 1.

Highest Common Factor of 945,506,612 using Euclid's algorithm

Highest Common Factor of 945,506,612 is 1

Step 1: Since 945 > 506, we apply the division lemma to 945 and 506, to get

945 = 506 x 1 + 439

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 439 and 506, to get

506 = 439 x 1 + 67

Step 3: We consider the new divisor 439 and the new remainder 67, and apply the division lemma to get

439 = 67 x 6 + 37

We consider the new divisor 67 and the new remainder 37,and apply the division lemma to get

67 = 37 x 1 + 30

We consider the new divisor 37 and the new remainder 30,and apply the division lemma to get

37 = 30 x 1 + 7

We consider the new divisor 30 and the new remainder 7,and apply the division lemma to get

30 = 7 x 4 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 945 and 506 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(30,7) = HCF(37,30) = HCF(67,37) = HCF(439,67) = HCF(506,439) = HCF(945,506) .

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

Step 1: Since 612 > 1, we apply the division lemma to 612 and 1, to get

612 = 1 x 612 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 612 is 1

Notice that 1 = HCF(612,1) .

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Frequently Asked Questions on HCF of 945, 506, 612 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, 506, 612?

Answer: HCF of 945, 506, 612 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 945, 506, 612 using Euclid's Algorithm?

Answer: For arbitrary numbers 945, 506, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.