Highest Common Factor of 665, 841, 14 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 665, 841, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 841, 14 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 665, 841, 14 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 665, 841, 14 is 1.

HCF(665, 841, 14) = 1

HCF of 665, 841, 14 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 665, 841, 14 is 1.

Highest Common Factor of 665,841,14 using Euclid's algorithm

Highest Common Factor of 665,841,14 is 1

Step 1: Since 841 > 665, we apply the division lemma to 841 and 665, to get

841 = 665 x 1 + 176

Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 176 and 665, to get

665 = 176 x 3 + 137

Step 3: We consider the new divisor 176 and the new remainder 137, and apply the division lemma to get

176 = 137 x 1 + 39

We consider the new divisor 137 and the new remainder 39,and apply the division lemma to get

137 = 39 x 3 + 20

We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get

39 = 20 x 1 + 19

We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get

20 = 19 x 1 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 841 is 1

Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(137,39) = HCF(176,137) = HCF(665,176) = HCF(841,665) .

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

Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1

Notice that 1 = HCF(14,1) .

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Frequently Asked Questions on HCF of 665, 841, 14 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 665, 841, 14?

Answer: HCF of 665, 841, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 841, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 841, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.