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 559, 753, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 559, 753, 409 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 559, 753, 409 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 559, 753, 409 is 1.
HCF(559, 753, 409) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 559, 753, 409 is 1.
Step 1: Since 753 > 559, we apply the division lemma to 753 and 559, to get
753 = 559 x 1 + 194
Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 194 and 559, to get
559 = 194 x 2 + 171
Step 3: We consider the new divisor 194 and the new remainder 171, and apply the division lemma to get
194 = 171 x 1 + 23
We consider the new divisor 171 and the new remainder 23,and apply the division lemma to get
171 = 23 x 7 + 10
We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get
23 = 10 x 2 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 559 and 753 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(171,23) = HCF(194,171) = HCF(559,194) = HCF(753,559) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 409 > 1, we apply the division lemma to 409 and 1, to get
409 = 1 x 409 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 409 is 1
Notice that 1 = HCF(409,1) .
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 559, 753, 409?
Answer: HCF of 559, 753, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 559, 753, 409 using Euclid's Algorithm?
Answer: For arbitrary numbers 559, 753, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.