Highest Common Factor of 465, 300, 667 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 465, 300, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 300, 667 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 465, 300, 667 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 465, 300, 667 is 1.
HCF(465, 300, 667) = 1
HCF of 465, 300, 667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 300, 667 is 1.
Highest Common Factor of 465,300,667 is 1
Step 1: Since 465 > 300, we apply the division lemma to 465 and 300, to get
465 = 300 x 1 + 165
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 165 and 300, to get
300 = 165 x 1 + 135
Step 3: We consider the new divisor 165 and the new remainder 135, and apply the division lemma to get
165 = 135 x 1 + 30
We consider the new divisor 135 and the new remainder 30,and apply the division lemma to get
135 = 30 x 4 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 465 and 300 is 15
Notice that 15 = HCF(30,15) = HCF(135,30) = HCF(165,135) = HCF(300,165) = HCF(465,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 667 > 15, we apply the division lemma to 667 and 15, to get
667 = 15 x 44 + 7
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 7 and 15, to get
15 = 7 x 2 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 667 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(667,15) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 465, 300, 667 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 465, 300, 667?
Answer: HCF of 465, 300, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 300, 667 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 300, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.