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, 134, 284 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 603, 134, 284 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, 134, 284 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, 134, 284 is 1.
HCF(603, 134, 284) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 603, 134, 284 is 1.
Step 1: Since 603 > 134, we apply the division lemma to 603 and 134, to get
603 = 134 x 4 + 67
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 67 and 134, to get
134 = 67 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 67, the HCF of 603 and 134 is 67
Notice that 67 = HCF(134,67) = HCF(603,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 284 > 67, we apply the division lemma to 284 and 67, to get
284 = 67 x 4 + 16
Step 2: Since the reminder 67 ≠ 0, we apply division lemma to 16 and 67, to get
67 = 16 x 4 + 3
Step 3: We consider the new divisor 16 and the new remainder 3, and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 67 and 284 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(67,16) = HCF(284,67) .
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, 134, 284?
Answer: HCF of 603, 134, 284 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 603, 134, 284 using Euclid's Algorithm?
Answer: For arbitrary numbers 603, 134, 284 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.