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, 435, 914, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 435, 914, 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 645, 435, 914, 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 645, 435, 914, 658 is 1.
HCF(645, 435, 914, 658) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 435, 914, 658 is 1.
Step 1: Since 645 > 435, we apply the division lemma to 645 and 435, to get
645 = 435 x 1 + 210
Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 210 and 435, to get
435 = 210 x 2 + 15
Step 3: We consider the new divisor 210 and the new remainder 15, and apply the division lemma to get
210 = 15 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 645 and 435 is 15
Notice that 15 = HCF(210,15) = HCF(435,210) = HCF(645,435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 914 > 15, we apply the division lemma to 914 and 15, to get
914 = 15 x 60 + 14
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 14 and 15, to get
15 = 14 x 1 + 1
Step 3: We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 914 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(914,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 658 > 1, we apply the division lemma to 658 and 1, to get
658 = 1 x 658 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 658 is 1
Notice that 1 = HCF(658,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 435, 914, 658?
Answer: HCF of 645, 435, 914, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 435, 914, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 435, 914, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.