Highest Common Factor of 780, 559, 672 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 780, 559, 672 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 780, 559, 672 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 780, 559, 672 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 780, 559, 672 is 1.

HCF(780, 559, 672) = 1

HCF of 780, 559, 672 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 780, 559, 672 is 1.

Highest Common Factor of 780,559,672 using Euclid's algorithm

Highest Common Factor of 780,559,672 is 1

Step 1: Since 780 > 559, we apply the division lemma to 780 and 559, to get

780 = 559 x 1 + 221

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 221 and 559, to get

559 = 221 x 2 + 117

Step 3: We consider the new divisor 221 and the new remainder 117, and apply the division lemma to get

221 = 117 x 1 + 104

We consider the new divisor 117 and the new remainder 104,and apply the division lemma to get

117 = 104 x 1 + 13

We consider the new divisor 104 and the new remainder 13,and apply the division lemma to get

104 = 13 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 780 and 559 is 13

Notice that 13 = HCF(104,13) = HCF(117,104) = HCF(221,117) = HCF(559,221) = HCF(780,559) .

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

Step 1: Since 672 > 13, we apply the division lemma to 672 and 13, to get

672 = 13 x 51 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 672 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(672,13) .

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Frequently Asked Questions on HCF of 780, 559, 672 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 780, 559, 672?

Answer: HCF of 780, 559, 672 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 780, 559, 672 using Euclid's Algorithm?

Answer: For arbitrary numbers 780, 559, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.