Highest Common Factor of 564, 789, 34 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 564, 789, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 789, 34 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 564, 789, 34 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 564, 789, 34 is 1.
HCF(564, 789, 34) = 1
HCF of 564, 789, 34 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 789, 34 is 1.
Highest Common Factor of 564,789,34 is 1
Step 1: Since 789 > 564, we apply the division lemma to 789 and 564, to get
789 = 564 x 1 + 225
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 225 and 564, to get
564 = 225 x 2 + 114
Step 3: We consider the new divisor 225 and the new remainder 114, and apply the division lemma to get
225 = 114 x 1 + 111
We consider the new divisor 114 and the new remainder 111,and apply the division lemma to get
114 = 111 x 1 + 3
We consider the new divisor 111 and the new remainder 3,and apply the division lemma to get
111 = 3 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 564 and 789 is 3
Notice that 3 = HCF(111,3) = HCF(114,111) = HCF(225,114) = HCF(564,225) = HCF(789,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34 > 3, we apply the division lemma to 34 and 3, to get
34 = 3 x 11 + 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 34 is 1
Notice that 1 = HCF(3,1) = HCF(34,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 564, 789, 34 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 564, 789, 34?
Answer: HCF of 564, 789, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 789, 34 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 789, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.