Highest Common Factor of 75, 720, 456, 884 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 75, 720, 456, 884 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 75, 720, 456, 884 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 75, 720, 456, 884 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 75, 720, 456, 884 is 1.

HCF(75, 720, 456, 884) = 1

HCF of 75, 720, 456, 884 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 75, 720, 456, 884 is 1.

Highest Common Factor of 75,720,456,884 using Euclid's algorithm

Highest Common Factor of 75,720,456,884 is 1

Step 1: Since 720 > 75, we apply the division lemma to 720 and 75, to get

720 = 75 x 9 + 45

Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 45 and 75, to get

75 = 45 x 1 + 30

Step 3: We consider the new divisor 45 and the new remainder 30, and apply the division lemma to get

45 = 30 x 1 + 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 75 and 720 is 15

Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) = HCF(720,75) .

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

Step 1: Since 456 > 15, we apply the division lemma to 456 and 15, to get

456 = 15 x 30 + 6

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get

15 = 6 x 2 + 3

Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 456 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(456,15) .

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

Step 1: Since 884 > 3, we apply the division lemma to 884 and 3, to get

884 = 3 x 294 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 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 3 and 884 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(884,3) .

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Frequently Asked Questions on HCF of 75, 720, 456, 884 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 75, 720, 456, 884?

Answer: HCF of 75, 720, 456, 884 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 75, 720, 456, 884 using Euclid's Algorithm?

Answer: For arbitrary numbers 75, 720, 456, 884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.