Highest Common Factor of 645, 785, 462, 645 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 645, 785, 462, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 785, 462, 645 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 645, 785, 462, 645 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 645, 785, 462, 645 is 1.
HCF(645, 785, 462, 645) = 1
HCF of 645, 785, 462, 645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 785, 462, 645 is 1.
Highest Common Factor of 645,785,462,645 is 1
Step 1: Since 785 > 645, we apply the division lemma to 785 and 645, to get
785 = 645 x 1 + 140
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 140 and 645, to get
645 = 140 x 4 + 85
Step 3: We consider the new divisor 140 and the new remainder 85, and apply the division lemma to get
140 = 85 x 1 + 55
We consider the new divisor 85 and the new remainder 55,and apply the division lemma to get
85 = 55 x 1 + 30
We consider the new divisor 55 and the new remainder 30,and apply the division lemma to get
55 = 30 x 1 + 25
We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 645 and 785 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(55,30) = HCF(85,55) = HCF(140,85) = HCF(645,140) = HCF(785,645) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 5, we apply the division lemma to 462 and 5, to get
462 = 5 x 92 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 462 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(462,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get
645 = 1 x 645 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1
Notice that 1 = HCF(645,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 645, 785, 462, 645 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 645, 785, 462, 645?
Answer: HCF of 645, 785, 462, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 785, 462, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 785, 462, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.