Highest Common Factor of 270, 986, 678 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 270, 986, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 986, 678 is 2 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 270, 986, 678 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 270, 986, 678 is 2.
HCF(270, 986, 678) = 2
HCF of 270, 986, 678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 986, 678 is 2.
Highest Common Factor of 270,986,678 is 2
Step 1: Since 986 > 270, we apply the division lemma to 986 and 270, to get
986 = 270 x 3 + 176
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 176 and 270, to get
270 = 176 x 1 + 94
Step 3: We consider the new divisor 176 and the new remainder 94, and apply the division lemma to get
176 = 94 x 1 + 82
We consider the new divisor 94 and the new remainder 82,and apply the division lemma to get
94 = 82 x 1 + 12
We consider the new divisor 82 and the new remainder 12,and apply the division lemma to get
82 = 12 x 6 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 270 and 986 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(82,12) = HCF(94,82) = HCF(176,94) = HCF(270,176) = HCF(986,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 2, we apply the division lemma to 678 and 2, to get
678 = 2 x 339 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 678 is 2
Notice that 2 = HCF(678,2) .
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Frequently Asked Questions on HCF of 270, 986, 678 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 270, 986, 678?
Answer: HCF of 270, 986, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 986, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 986, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.