Highest Common Factor of 448, 709, 107 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 448, 709, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 448, 709, 107 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 448, 709, 107 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 448, 709, 107 is 1.

HCF(448, 709, 107) = 1

HCF of 448, 709, 107 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 448, 709, 107 is 1.

Highest Common Factor of 448,709,107 using Euclid's algorithm

Highest Common Factor of 448,709,107 is 1

Step 1: Since 709 > 448, we apply the division lemma to 709 and 448, to get

709 = 448 x 1 + 261

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 261 and 448, to get

448 = 261 x 1 + 187

Step 3: We consider the new divisor 261 and the new remainder 187, and apply the division lemma to get

261 = 187 x 1 + 74

We consider the new divisor 187 and the new remainder 74,and apply the division lemma to get

187 = 74 x 2 + 39

We consider the new divisor 74 and the new remainder 39,and apply the division lemma to get

74 = 39 x 1 + 35

We consider the new divisor 39 and the new remainder 35,and apply the division lemma to get

39 = 35 x 1 + 4

We consider the new divisor 35 and the new remainder 4,and apply the division lemma to get

35 = 4 x 8 + 3

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

4 = 3 x 1 + 1

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 448 and 709 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(35,4) = HCF(39,35) = HCF(74,39) = HCF(187,74) = HCF(261,187) = HCF(448,261) = HCF(709,448) .

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

Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get

107 = 1 x 107 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1

Notice that 1 = HCF(107,1) .

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Frequently Asked Questions on HCF of 448, 709, 107 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 448, 709, 107?

Answer: HCF of 448, 709, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 448, 709, 107 using Euclid's Algorithm?

Answer: For arbitrary numbers 448, 709, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.