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 690, 978, 271 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 978, 271 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 690, 978, 271 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 690, 978, 271 is 1.
HCF(690, 978, 271) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 978, 271 is 1.
Step 1: Since 978 > 690, we apply the division lemma to 978 and 690, to get
978 = 690 x 1 + 288
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 288 and 690, to get
690 = 288 x 2 + 114
Step 3: We consider the new divisor 288 and the new remainder 114, and apply the division lemma to get
288 = 114 x 2 + 60
We consider the new divisor 114 and the new remainder 60,and apply the division lemma to get
114 = 60 x 1 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 690 and 978 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(114,60) = HCF(288,114) = HCF(690,288) = HCF(978,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 271 > 6, we apply the division lemma to 271 and 6, to get
271 = 6 x 45 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 271 is 1
Notice that 1 = HCF(6,1) = HCF(271,6) .
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 690, 978, 271?
Answer: HCF of 690, 978, 271 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 978, 271 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 978, 271 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.