Highest Common Factor of 257, 980, 975, 15 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 257, 980, 975, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 980, 975, 15 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, 980, 975, 15 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, 980, 975, 15 is 1.
HCF(257, 980, 975, 15) = 1
HCF of 257, 980, 975, 15 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 257, 980, 975, 15 is 1.
Highest Common Factor of 257,980,975,15 is 1
Step 1: Since 980 > 257, we apply the division lemma to 980 and 257, to get
980 = 257 x 3 + 209
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 209 and 257, to get
257 = 209 x 1 + 48
Step 3: We consider the new divisor 209 and the new remainder 48, and apply the division lemma to get
209 = 48 x 4 + 17
We consider the new divisor 48 and the new remainder 17,and apply the division lemma to get
48 = 17 x 2 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 257 and 980 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(48,17) = HCF(209,48) = HCF(257,209) = HCF(980,257) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 1, we apply the division lemma to 975 and 1, to get
975 = 1 x 975 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 975 is 1
Notice that 1 = HCF(975,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1
Notice that 1 = HCF(15,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 257, 980, 975, 15 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 257, 980, 975, 15?
Answer: HCF of 257, 980, 975, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 980, 975, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 980, 975, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.