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 2255, 6474, 55513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2255, 6474, 55513 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 2255, 6474, 55513 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 2255, 6474, 55513 is 1.
HCF(2255, 6474, 55513) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2255, 6474, 55513 is 1.
Step 1: Since 6474 > 2255, we apply the division lemma to 6474 and 2255, to get
6474 = 2255 x 2 + 1964
Step 2: Since the reminder 2255 ≠ 0, we apply division lemma to 1964 and 2255, to get
2255 = 1964 x 1 + 291
Step 3: We consider the new divisor 1964 and the new remainder 291, and apply the division lemma to get
1964 = 291 x 6 + 218
We consider the new divisor 291 and the new remainder 218,and apply the division lemma to get
291 = 218 x 1 + 73
We consider the new divisor 218 and the new remainder 73,and apply the division lemma to get
218 = 73 x 2 + 72
We consider the new divisor 73 and the new remainder 72,and apply the division lemma to get
73 = 72 x 1 + 1
We consider the new divisor 72 and the new remainder 1,and apply the division lemma to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2255 and 6474 is 1
Notice that 1 = HCF(72,1) = HCF(73,72) = HCF(218,73) = HCF(291,218) = HCF(1964,291) = HCF(2255,1964) = HCF(6474,2255) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55513 > 1, we apply the division lemma to 55513 and 1, to get
55513 = 1 x 55513 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55513 is 1
Notice that 1 = HCF(55513,1) .
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 2255, 6474, 55513?
Answer: HCF of 2255, 6474, 55513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2255, 6474, 55513 using Euclid's Algorithm?
Answer: For arbitrary numbers 2255, 6474, 55513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.