Highest Common Factor of 679, 948, 421 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 679, 948, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 679, 948, 421 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 679, 948, 421 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 679, 948, 421 is 1.

HCF(679, 948, 421) = 1

HCF of 679, 948, 421 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 679, 948, 421 is 1.

Highest Common Factor of 679,948,421 using Euclid's algorithm

Highest Common Factor of 679,948,421 is 1

Step 1: Since 948 > 679, we apply the division lemma to 948 and 679, to get

948 = 679 x 1 + 269

Step 2: Since the reminder 679 ≠ 0, we apply division lemma to 269 and 679, to get

679 = 269 x 2 + 141

Step 3: We consider the new divisor 269 and the new remainder 141, and apply the division lemma to get

269 = 141 x 1 + 128

We consider the new divisor 141 and the new remainder 128,and apply the division lemma to get

141 = 128 x 1 + 13

We consider the new divisor 128 and the new remainder 13,and apply the division lemma to get

128 = 13 x 9 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 679 and 948 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(128,13) = HCF(141,128) = HCF(269,141) = HCF(679,269) = HCF(948,679) .

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

Step 1: Since 421 > 1, we apply the division lemma to 421 and 1, to get

421 = 1 x 421 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 421 is 1

Notice that 1 = HCF(421,1) .

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Frequently Asked Questions on HCF of 679, 948, 421 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 679, 948, 421?

Answer: HCF of 679, 948, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 679, 948, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 679, 948, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.