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 603, 373, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 603, 373, 509 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 603, 373, 509 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 603, 373, 509 is 1.
HCF(603, 373, 509) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 603, 373, 509 is 1.
Step 1: Since 603 > 373, we apply the division lemma to 603 and 373, to get
603 = 373 x 1 + 230
Step 2: Since the reminder 373 ≠ 0, we apply division lemma to 230 and 373, to get
373 = 230 x 1 + 143
Step 3: We consider the new divisor 230 and the new remainder 143, and apply the division lemma to get
230 = 143 x 1 + 87
We consider the new divisor 143 and the new remainder 87,and apply the division lemma to get
143 = 87 x 1 + 56
We consider the new divisor 87 and the new remainder 56,and apply the division lemma to get
87 = 56 x 1 + 31
We consider the new divisor 56 and the new remainder 31,and apply the division lemma to get
56 = 31 x 1 + 25
We consider the new divisor 31 and the new remainder 25,and apply the division lemma to get
31 = 25 x 1 + 6
We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get
25 = 6 x 4 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 603 and 373 is 1
Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(31,25) = HCF(56,31) = HCF(87,56) = HCF(143,87) = HCF(230,143) = HCF(373,230) = HCF(603,373) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 509 > 1, we apply the division lemma to 509 and 1, to get
509 = 1 x 509 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 509 is 1
Notice that 1 = HCF(509,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 603, 373, 509?
Answer: HCF of 603, 373, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 603, 373, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 603, 373, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.