Highest Common Factor of 714, 966, 725 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 714, 966, 725 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 966, 725 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 714, 966, 725 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 714, 966, 725 is 1.

HCF(714, 966, 725) = 1

HCF of 714, 966, 725 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 714, 966, 725 is 1.

Highest Common Factor of 714,966,725 using Euclid's algorithm

Highest Common Factor of 714,966,725 is 1

Step 1: Since 966 > 714, we apply the division lemma to 966 and 714, to get

966 = 714 x 1 + 252

Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 252 and 714, to get

714 = 252 x 2 + 210

Step 3: We consider the new divisor 252 and the new remainder 210, and apply the division lemma to get

252 = 210 x 1 + 42

We consider the new divisor 210 and the new remainder 42, and apply the division lemma to get

210 = 42 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 714 and 966 is 42

Notice that 42 = HCF(210,42) = HCF(252,210) = HCF(714,252) = HCF(966,714) .

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

Step 1: Since 725 > 42, we apply the division lemma to 725 and 42, to get

725 = 42 x 17 + 11

Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 11 and 42, to get

42 = 11 x 3 + 9

Step 3: We consider the new divisor 11 and the new remainder 9, and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 42 and 725 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(42,11) = HCF(725,42) .

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Frequently Asked Questions on HCF of 714, 966, 725 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 714, 966, 725?

Answer: HCF of 714, 966, 725 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 966, 725 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 966, 725 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.