Highest Common Factor of 600, 165, 164, 283 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 600, 165, 164, 283 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 165, 164, 283 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 600, 165, 164, 283 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 600, 165, 164, 283 is 1.
HCF(600, 165, 164, 283) = 1
HCF of 600, 165, 164, 283 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 600, 165, 164, 283 is 1.
Highest Common Factor of 600,165,164,283 is 1
Step 1: Since 600 > 165, we apply the division lemma to 600 and 165, to get
600 = 165 x 3 + 105
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 105 and 165, to get
165 = 105 x 1 + 60
Step 3: We consider the new divisor 105 and the new remainder 60, and apply the division lemma to get
105 = 60 x 1 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 600 and 165 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(105,60) = HCF(165,105) = HCF(600,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 164 > 15, we apply the division lemma to 164 and 15, to get
164 = 15 x 10 + 14
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 14 and 15, to get
15 = 14 x 1 + 1
Step 3: We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 164 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(164,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 283 > 1, we apply the division lemma to 283 and 1, to get
283 = 1 x 283 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 283 is 1
Notice that 1 = HCF(283,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 600, 165, 164, 283 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 600, 165, 164, 283?
Answer: HCF of 600, 165, 164, 283 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 165, 164, 283 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 165, 164, 283 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.