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 804, 685, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 804, 685, 121 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 804, 685, 121 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 804, 685, 121 is 1.
HCF(804, 685, 121) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 804, 685, 121 is 1.
Step 1: Since 804 > 685, we apply the division lemma to 804 and 685, to get
804 = 685 x 1 + 119
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 119 and 685, to get
685 = 119 x 5 + 90
Step 3: We consider the new divisor 119 and the new remainder 90, and apply the division lemma to get
119 = 90 x 1 + 29
We consider the new divisor 90 and the new remainder 29,and apply the division lemma to get
90 = 29 x 3 + 3
We consider the new divisor 29 and the new remainder 3,and apply the division lemma to get
29 = 3 x 9 + 2
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 804 and 685 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) = HCF(90,29) = HCF(119,90) = HCF(685,119) = HCF(804,685) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 121 > 1, we apply the division lemma to 121 and 1, to get
121 = 1 x 121 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 121 is 1
Notice that 1 = HCF(121,1) .
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 804, 685, 121?
Answer: HCF of 804, 685, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 804, 685, 121 using Euclid's Algorithm?
Answer: For arbitrary numbers 804, 685, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.