Highest Common Factor of 121, 704 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 121, 704 i.e. 11 the largest integer that leaves a remainder zero for all numbers.

HCF of 121, 704 is 11 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 121, 704 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 121, 704 is 11.

HCF(121, 704) = 11

HCF of 121, 704 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 121, 704 is 11.

Highest Common Factor of 121,704 using Euclid's algorithm

Highest Common Factor of 121,704 is 11

Step 1: Since 704 > 121, we apply the division lemma to 704 and 121, to get

704 = 121 x 5 + 99

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 99 and 121, to get

121 = 99 x 1 + 22

Step 3: We consider the new divisor 99 and the new remainder 22, and apply the division lemma to get

99 = 22 x 4 + 11

We consider the new divisor 22 and the new remainder 11, and apply the division lemma to get

22 = 11 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 121 and 704 is 11

Notice that 11 = HCF(22,11) = HCF(99,22) = HCF(121,99) = HCF(704,121) .

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Frequently Asked Questions on HCF of 121, 704 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 121, 704?

Answer: HCF of 121, 704 is 11 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 121, 704 using Euclid's Algorithm?

Answer: For arbitrary numbers 121, 704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.