Highest Common Factor of 961, 606, 136, 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 961, 606, 136, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 961, 606, 136, 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 961, 606, 136, 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 961, 606, 136, 14 is 1.

HCF(961, 606, 136, 14) = 1

HCF of 961, 606, 136, 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 961, 606, 136, 14 is 1.

Highest Common Factor of 961,606,136,14 using Euclid's algorithm

Highest Common Factor of 961,606,136,14 is 1

Step 1: Since 961 > 606, we apply the division lemma to 961 and 606, to get

961 = 606 x 1 + 355

Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 355 and 606, to get

606 = 355 x 1 + 251

Step 3: We consider the new divisor 355 and the new remainder 251, and apply the division lemma to get

355 = 251 x 1 + 104

We consider the new divisor 251 and the new remainder 104,and apply the division lemma to get

251 = 104 x 2 + 43

We consider the new divisor 104 and the new remainder 43,and apply the division lemma to get

104 = 43 x 2 + 18

We consider the new divisor 43 and the new remainder 18,and apply the division lemma to get

43 = 18 x 2 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 961 and 606 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(43,18) = HCF(104,43) = HCF(251,104) = HCF(355,251) = HCF(606,355) = HCF(961,606) .

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

Step 1: Since 136 > 1, we apply the division lemma to 136 and 1, to get

136 = 1 x 136 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 136 is 1

Notice that 1 = HCF(136,1) .

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 961, 606, 136, 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 961, 606, 136, 14?

Answer: HCF of 961, 606, 136, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 961, 606, 136, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 961, 606, 136, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.