Highest Common Factor of 597, 666 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 597, 666 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 597, 666 is 3 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 597, 666 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 597, 666 is 3.
HCF(597, 666) = 3
HCF of 597, 666 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 597, 666 is 3.
Highest Common Factor of 597,666 is 3
Step 1: Since 666 > 597, we apply the division lemma to 666 and 597, to get
666 = 597 x 1 + 69
Step 2: Since the reminder 597 ≠ 0, we apply division lemma to 69 and 597, to get
597 = 69 x 8 + 45
Step 3: We consider the new divisor 69 and the new remainder 45, and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 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 597 and 666 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(597,69) = HCF(666,597) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 597, 666 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 597, 666?
Answer: HCF of 597, 666 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 597, 666 using Euclid's Algorithm?
Answer: For arbitrary numbers 597, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.