Highest Common Factor of 180, 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 180, 678 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 678 is 6 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 180, 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 180, 678 is 6.
HCF(180, 678) = 6
HCF of 180, 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 180, 678 is 6.
Highest Common Factor of 180,678 is 6
Step 1: Since 678 > 180, we apply the division lemma to 678 and 180, to get
678 = 180 x 3 + 138
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 138 and 180, to get
180 = 138 x 1 + 42
Step 3: We consider the new divisor 138 and the new remainder 42, and apply the division lemma to get
138 = 42 x 3 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 180 and 678 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(138,42) = HCF(180,138) = HCF(678,180) .
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Frequently Asked Questions on HCF of 180, 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 180, 678?
Answer: HCF of 180, 678 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.