Highest Common Factor of 610, 664 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 610, 664 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 664 is 2 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 610, 664 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 610, 664 is 2.
HCF(610, 664) = 2
HCF of 610, 664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 610, 664 is 2.
Highest Common Factor of 610,664 is 2
Step 1: Since 664 > 610, we apply the division lemma to 664 and 610, to get
664 = 610 x 1 + 54
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 54 and 610, to get
610 = 54 x 11 + 16
Step 3: We consider the new divisor 54 and the new remainder 16, and apply the division lemma to get
54 = 16 x 3 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 610 and 664 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(54,16) = HCF(610,54) = HCF(664,610) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 610, 664 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 610, 664?
Answer: HCF of 610, 664 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.