Highest Common Factor of 945, 486, 314 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 945, 486, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 486, 314 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 945, 486, 314 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 945, 486, 314 is 1.
HCF(945, 486, 314) = 1
HCF of 945, 486, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 486, 314 is 1.
Highest Common Factor of 945,486,314 is 1
Step 1: Since 945 > 486, we apply the division lemma to 945 and 486, to get
945 = 486 x 1 + 459
Step 2: Since the reminder 486 ≠ 0, we apply division lemma to 459 and 486, to get
486 = 459 x 1 + 27
Step 3: We consider the new divisor 459 and the new remainder 27, and apply the division lemma to get
459 = 27 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 945 and 486 is 27
Notice that 27 = HCF(459,27) = HCF(486,459) = HCF(945,486) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 27, we apply the division lemma to 314 and 27, to get
314 = 27 x 11 + 17
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 17 and 27, to get
27 = 17 x 1 + 10
Step 3: We consider the new divisor 17 and the new remainder 10, and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 27 and 314 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(314,27) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 945, 486, 314 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 945, 486, 314?
Answer: HCF of 945, 486, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 486, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 486, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.