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
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) 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) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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.