Highest Common Factor of 600, 350, 20, 882 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, 350, 20, 882 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 350, 20, 882 is 2 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, 350, 20, 882 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, 350, 20, 882 is 2.
HCF(600, 350, 20, 882) = 2
HCF of 600, 350, 20, 882 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, 350, 20, 882 is 2.
Highest Common Factor of 600,350,20,882 is 2
Step 1: Since 600 > 350, we apply the division lemma to 600 and 350, to get
600 = 350 x 1 + 250
Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 250 and 350, to get
350 = 250 x 1 + 100
Step 3: We consider the new divisor 250 and the new remainder 100, and apply the division lemma to get
250 = 100 x 2 + 50
We consider the new divisor 100 and the new remainder 50, and apply the division lemma to get
100 = 50 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 600 and 350 is 50
Notice that 50 = HCF(100,50) = HCF(250,100) = HCF(350,250) = HCF(600,350) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 50 > 20, we apply the division lemma to 50 and 20, to get
50 = 20 x 2 + 10
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 50 and 20 is 10
Notice that 10 = HCF(20,10) = HCF(50,20) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 882 > 10, we apply the division lemma to 882 and 10, to get
882 = 10 x 88 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 882 is 2
Notice that 2 = HCF(10,2) = HCF(882,10) .
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, 350, 20, 882 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, 350, 20, 882?
Answer: HCF of 600, 350, 20, 882 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 350, 20, 882 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 350, 20, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.