Highest Common Factor of 985, 645, 688, 719 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 985, 645, 688, 719 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 985, 645, 688, 719 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 985, 645, 688, 719 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 985, 645, 688, 719 is 1.

HCF(985, 645, 688, 719) = 1

HCF of 985, 645, 688, 719 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 985, 645, 688, 719 is 1.

Highest Common Factor of 985,645,688,719 using Euclid's algorithm

Highest Common Factor of 985,645,688,719 is 1

Step 1: Since 985 > 645, we apply the division lemma to 985 and 645, to get

985 = 645 x 1 + 340

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 340 and 645, to get

645 = 340 x 1 + 305

Step 3: We consider the new divisor 340 and the new remainder 305, and apply the division lemma to get

340 = 305 x 1 + 35

We consider the new divisor 305 and the new remainder 35,and apply the division lemma to get

305 = 35 x 8 + 25

We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get

35 = 25 x 1 + 10

We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get

25 = 10 x 2 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 985 and 645 is 5

Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(305,35) = HCF(340,305) = HCF(645,340) = HCF(985,645) .

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

Step 1: Since 688 > 5, we apply the division lemma to 688 and 5, to get

688 = 5 x 137 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 688 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(688,5) .

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

Step 1: Since 719 > 1, we apply the division lemma to 719 and 1, to get

719 = 1 x 719 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 719 is 1

Notice that 1 = HCF(719,1) .

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Frequently Asked Questions on HCF of 985, 645, 688, 719 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 985, 645, 688, 719?

Answer: HCF of 985, 645, 688, 719 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 985, 645, 688, 719 using Euclid's Algorithm?

Answer: For arbitrary numbers 985, 645, 688, 719 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.