Highest Common Factor of 684, 448, 758 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 684, 448, 758 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 448, 758 is 2 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 684, 448, 758 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 684, 448, 758 is 2.

HCF(684, 448, 758) = 2

HCF of 684, 448, 758 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 684, 448, 758 is 2.

Highest Common Factor of 684,448,758 using Euclid's algorithm

Highest Common Factor of 684,448,758 is 2

Step 1: Since 684 > 448, we apply the division lemma to 684 and 448, to get

684 = 448 x 1 + 236

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 236 and 448, to get

448 = 236 x 1 + 212

Step 3: We consider the new divisor 236 and the new remainder 212, and apply the division lemma to get

236 = 212 x 1 + 24

We consider the new divisor 212 and the new remainder 24,and apply the division lemma to get

212 = 24 x 8 + 20

We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get

24 = 20 x 1 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 684 and 448 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(212,24) = HCF(236,212) = HCF(448,236) = HCF(684,448) .

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

Step 1: Since 758 > 4, we apply the division lemma to 758 and 4, to get

758 = 4 x 189 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 758 is 2

Notice that 2 = HCF(4,2) = HCF(758,4) .

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Frequently Asked Questions on HCF of 684, 448, 758 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 684, 448, 758?

Answer: HCF of 684, 448, 758 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 448, 758 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 448, 758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.