Highest Common Factor of 708, 965, 678 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 708, 965, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 708, 965, 678 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 708, 965, 678 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 708, 965, 678 is 1.

HCF(708, 965, 678) = 1

HCF of 708, 965, 678 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 708, 965, 678 is 1.

Highest Common Factor of 708,965,678 using Euclid's algorithm

Highest Common Factor of 708,965,678 is 1

Step 1: Since 965 > 708, we apply the division lemma to 965 and 708, to get

965 = 708 x 1 + 257

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 257 and 708, to get

708 = 257 x 2 + 194

Step 3: We consider the new divisor 257 and the new remainder 194, and apply the division lemma to get

257 = 194 x 1 + 63

We consider the new divisor 194 and the new remainder 63,and apply the division lemma to get

194 = 63 x 3 + 5

We consider the new divisor 63 and the new remainder 5,and apply the division lemma to get

63 = 5 x 12 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 708 and 965 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(63,5) = HCF(194,63) = HCF(257,194) = HCF(708,257) = HCF(965,708) .

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

Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get

678 = 1 x 678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1

Notice that 1 = HCF(678,1) .

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Frequently Asked Questions on HCF of 708, 965, 678 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 708, 965, 678?

Answer: HCF of 708, 965, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 708, 965, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 708, 965, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.