Highest Common Factor of 654, 465, 375 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 654, 465, 375 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 465, 375 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 654, 465, 375 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 654, 465, 375 is 3.
HCF(654, 465, 375) = 3
HCF of 654, 465, 375 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 465, 375 is 3.
Highest Common Factor of 654,465,375 is 3
Step 1: Since 654 > 465, we apply the division lemma to 654 and 465, to get
654 = 465 x 1 + 189
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 189 and 465, to get
465 = 189 x 2 + 87
Step 3: We consider the new divisor 189 and the new remainder 87, and apply the division lemma to get
189 = 87 x 2 + 15
We consider the new divisor 87 and the new remainder 15,and apply the division lemma to get
87 = 15 x 5 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 654 and 465 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(87,15) = HCF(189,87) = HCF(465,189) = HCF(654,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 375 > 3, we apply the division lemma to 375 and 3, to get
375 = 3 x 125 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 375 is 3
Notice that 3 = HCF(375,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 654, 465, 375 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 654, 465, 375?
Answer: HCF of 654, 465, 375 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 465, 375 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 465, 375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.