Highest Common Factor of 678, 910, 180 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 678, 910, 180 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 910, 180 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 678, 910, 180 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 678, 910, 180 is 2.
HCF(678, 910, 180) = 2
HCF of 678, 910, 180 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 910, 180 is 2.
Highest Common Factor of 678,910,180 is 2
Step 1: Since 910 > 678, we apply the division lemma to 910 and 678, to get
910 = 678 x 1 + 232
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 232 and 678, to get
678 = 232 x 2 + 214
Step 3: We consider the new divisor 232 and the new remainder 214, and apply the division lemma to get
232 = 214 x 1 + 18
We consider the new divisor 214 and the new remainder 18,and apply the division lemma to get
214 = 18 x 11 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 910 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(214,18) = HCF(232,214) = HCF(678,232) = HCF(910,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 180 > 2, we apply the division lemma to 180 and 2, to get
180 = 2 x 90 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 180 is 2
Notice that 2 = HCF(180,2) .
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Frequently Asked Questions on HCF of 678, 910, 180 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 678, 910, 180?
Answer: HCF of 678, 910, 180 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 910, 180 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 910, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.