Highest Common Factor of 54, 508, 960, 345 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 54, 508, 960, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 54, 508, 960, 345 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 54, 508, 960, 345 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 54, 508, 960, 345 is 1.
HCF(54, 508, 960, 345) = 1
HCF of 54, 508, 960, 345 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 54, 508, 960, 345 is 1.
Highest Common Factor of 54,508,960,345 is 1
Step 1: Since 508 > 54, we apply the division lemma to 508 and 54, to get
508 = 54 x 9 + 22
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 22 and 54, to get
54 = 22 x 2 + 10
Step 3: We consider the new divisor 22 and the new remainder 10, and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 54 and 508 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(508,54) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 960 > 2, we apply the division lemma to 960 and 2, to get
960 = 2 x 480 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 960 is 2
Notice that 2 = HCF(960,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 345 > 2, we apply the division lemma to 345 and 2, to get
345 = 2 x 172 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 345 is 1
Notice that 1 = HCF(2,1) = HCF(345,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 54, 508, 960, 345 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 54, 508, 960, 345?
Answer: HCF of 54, 508, 960, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 54, 508, 960, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 54, 508, 960, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.