Highest Common Factor of 600, 672, 814 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, 672, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 672, 814 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, 672, 814 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, 672, 814 is 2.
HCF(600, 672, 814) = 2
HCF of 600, 672, 814 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, 672, 814 is 2.
Highest Common Factor of 600,672,814 is 2
Step 1: Since 672 > 600, we apply the division lemma to 672 and 600, to get
672 = 600 x 1 + 72
Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 72 and 600, to get
600 = 72 x 8 + 24
Step 3: We consider the new divisor 72 and the new remainder 24, and apply the division lemma to get
72 = 24 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 600 and 672 is 24
Notice that 24 = HCF(72,24) = HCF(600,72) = HCF(672,600) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 24, we apply the division lemma to 814 and 24, to get
814 = 24 x 33 + 22
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 22 and 24, to get
24 = 22 x 1 + 2
Step 3: We consider the new divisor 22 and the new remainder 2, and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 24 and 814 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(814,24) .
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, 672, 814 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, 672, 814?
Answer: HCF of 600, 672, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 672, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 672, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.