Highest Common Factor of 528, 736, 755 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 528, 736, 755 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 528, 736, 755 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 528, 736, 755 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 528, 736, 755 is 1.

HCF(528, 736, 755) = 1

HCF of 528, 736, 755 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 528, 736, 755 is 1.

Highest Common Factor of 528,736,755 using Euclid's algorithm

Highest Common Factor of 528,736,755 is 1

Step 1: Since 736 > 528, we apply the division lemma to 736 and 528, to get

736 = 528 x 1 + 208

Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 208 and 528, to get

528 = 208 x 2 + 112

Step 3: We consider the new divisor 208 and the new remainder 112, and apply the division lemma to get

208 = 112 x 1 + 96

We consider the new divisor 112 and the new remainder 96,and apply the division lemma to get

112 = 96 x 1 + 16

We consider the new divisor 96 and the new remainder 16,and apply the division lemma to get

96 = 16 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 528 and 736 is 16

Notice that 16 = HCF(96,16) = HCF(112,96) = HCF(208,112) = HCF(528,208) = HCF(736,528) .

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

Step 1: Since 755 > 16, we apply the division lemma to 755 and 16, to get

755 = 16 x 47 + 3

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 3 and 16, to get

16 = 3 x 5 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 755 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(755,16) .

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Frequently Asked Questions on HCF of 528, 736, 755 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 528, 736, 755?

Answer: HCF of 528, 736, 755 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 528, 736, 755 using Euclid's Algorithm?

Answer: For arbitrary numbers 528, 736, 755 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.