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 970, 271, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 970, 271, 127 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 970, 271, 127 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 970, 271, 127 is 1.
HCF(970, 271, 127) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 970, 271, 127 is 1.
Step 1: Since 970 > 271, we apply the division lemma to 970 and 271, to get
970 = 271 x 3 + 157
Step 2: Since the reminder 271 ≠ 0, we apply division lemma to 157 and 271, to get
271 = 157 x 1 + 114
Step 3: We consider the new divisor 157 and the new remainder 114, and apply the division lemma to get
157 = 114 x 1 + 43
We consider the new divisor 114 and the new remainder 43,and apply the division lemma to get
114 = 43 x 2 + 28
We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get
43 = 28 x 1 + 15
We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get
28 = 15 x 1 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 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 970 and 271 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(114,43) = HCF(157,114) = HCF(271,157) = HCF(970,271) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 1, we apply the division lemma to 127 and 1, to get
127 = 1 x 127 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 127 is 1
Notice that 1 = HCF(127,1) .
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 970, 271, 127?
Answer: HCF of 970, 271, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 970, 271, 127 using Euclid's Algorithm?
Answer: For arbitrary numbers 970, 271, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.