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 257, 561, 185, 176 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 561, 185, 176 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 257, 561, 185, 176 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 257, 561, 185, 176 is 1.
HCF(257, 561, 185, 176) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 257, 561, 185, 176 is 1.
Step 1: Since 561 > 257, we apply the division lemma to 561 and 257, to get
561 = 257 x 2 + 47
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 47 and 257, to get
257 = 47 x 5 + 22
Step 3: We consider the new divisor 47 and the new remainder 22, and apply the division lemma to get
47 = 22 x 2 + 3
We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get
22 = 3 x 7 + 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 257 and 561 is 1
Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(47,22) = HCF(257,47) = HCF(561,257) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 185 > 1, we apply the division lemma to 185 and 1, to get
185 = 1 x 185 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 185 is 1
Notice that 1 = HCF(185,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 176 > 1, we apply the division lemma to 176 and 1, to get
176 = 1 x 176 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 176 is 1
Notice that 1 = HCF(176,1) .
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 257, 561, 185, 176?
Answer: HCF of 257, 561, 185, 176 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 561, 185, 176 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 561, 185, 176 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.