Highest Common Factor of 561, 669, 589 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 561, 669, 589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 669, 589 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 561, 669, 589 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 561, 669, 589 is 1.
HCF(561, 669, 589) = 1
HCF of 561, 669, 589 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 669, 589 is 1.
Highest Common Factor of 561,669,589 is 1
Step 1: Since 669 > 561, we apply the division lemma to 669 and 561, to get
669 = 561 x 1 + 108
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 108 and 561, to get
561 = 108 x 5 + 21
Step 3: We consider the new divisor 108 and the new remainder 21, and apply the division lemma to get
108 = 21 x 5 + 3
We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 669 is 3
Notice that 3 = HCF(21,3) = HCF(108,21) = HCF(561,108) = HCF(669,561) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 589 > 3, we apply the division lemma to 589 and 3, to get
589 = 3 x 196 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 589 is 1
Notice that 1 = HCF(3,1) = HCF(589,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 561, 669, 589 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 561, 669, 589?
Answer: HCF of 561, 669, 589 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 669, 589 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 669, 589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.