Highest Common Factor of 306, 659, 705, 803 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 306, 659, 705, 803 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 659, 705, 803 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 306, 659, 705, 803 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 306, 659, 705, 803 is 1.
HCF(306, 659, 705, 803) = 1
HCF of 306, 659, 705, 803 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 659, 705, 803 is 1.
Highest Common Factor of 306,659,705,803 is 1
Step 1: Since 659 > 306, we apply the division lemma to 659 and 306, to get
659 = 306 x 2 + 47
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 47 and 306, to get
306 = 47 x 6 + 24
Step 3: We consider the new divisor 47 and the new remainder 24, and apply the division lemma to get
47 = 24 x 1 + 23
We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get
24 = 23 x 1 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 306 and 659 is 1
Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(306,47) = HCF(659,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get
705 = 1 x 705 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1
Notice that 1 = HCF(705,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 803 > 1, we apply the division lemma to 803 and 1, to get
803 = 1 x 803 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 803 is 1
Notice that 1 = HCF(803,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 306, 659, 705, 803 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 306, 659, 705, 803?
Answer: HCF of 306, 659, 705, 803 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 659, 705, 803 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 659, 705, 803 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.