Highest Common Factor of 345, 921, 658 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 345, 921, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 921, 658 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 345, 921, 658 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 345, 921, 658 is 1.
HCF(345, 921, 658) = 1
HCF of 345, 921, 658 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 921, 658 is 1.
Highest Common Factor of 345,921,658 is 1
Step 1: Since 921 > 345, we apply the division lemma to 921 and 345, to get
921 = 345 x 2 + 231
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 231 and 345, to get
345 = 231 x 1 + 114
Step 3: We consider the new divisor 231 and the new remainder 114, and apply the division lemma to get
231 = 114 x 2 + 3
We consider the new divisor 114 and the new remainder 3, and apply the division lemma to get
114 = 3 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 921 is 3
Notice that 3 = HCF(114,3) = HCF(231,114) = HCF(345,231) = HCF(921,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 658 > 3, we apply the division lemma to 658 and 3, to get
658 = 3 x 219 + 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 658 is 1
Notice that 1 = HCF(3,1) = HCF(658,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 345, 921, 658 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 345, 921, 658?
Answer: HCF of 345, 921, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 921, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 921, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
