Highest Common Factor of 735, 343, 804 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 735, 343, 804 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 343, 804 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 735, 343, 804 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 735, 343, 804 is 1.
HCF(735, 343, 804) = 1
HCF of 735, 343, 804 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 343, 804 is 1.
Highest Common Factor of 735,343,804 is 1
Step 1: Since 735 > 343, we apply the division lemma to 735 and 343, to get
735 = 343 x 2 + 49
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 49 and 343, to get
343 = 49 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 49, the HCF of 735 and 343 is 49
Notice that 49 = HCF(343,49) = HCF(735,343) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 804 > 49, we apply the division lemma to 804 and 49, to get
804 = 49 x 16 + 20
Step 2: Since the reminder 49 ≠ 0, we apply division lemma to 20 and 49, to get
49 = 20 x 2 + 9
Step 3: We consider the new divisor 20 and the new remainder 9, and apply the division lemma to get
20 = 9 x 2 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 49 and 804 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(49,20) = HCF(804,49) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 735, 343, 804 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 735, 343, 804?
Answer: HCF of 735, 343, 804 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 343, 804 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 343, 804 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
