Highest Common Factor of 678, 1980 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, 1980 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 1980 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 678, 1980 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, 1980 is 6.
HCF(678, 1980) = 6
HCF of 678, 1980 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, 1980 is 6.
Highest Common Factor of 678,1980 is 6
Step 1: Since 1980 > 678, we apply the division lemma to 1980 and 678, to get
1980 = 678 x 2 + 624
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 624 and 678, to get
678 = 624 x 1 + 54
Step 3: We consider the new divisor 624 and the new remainder 54, and apply the division lemma to get
624 = 54 x 11 + 30
We consider the new divisor 54 and the new remainder 30,and apply the division lemma to get
54 = 30 x 1 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 678 and 1980 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(624,54) = HCF(678,624) = HCF(1980,678) .
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Frequently Asked Questions on HCF of 678, 1980 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, 1980?
Answer: HCF of 678, 1980 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 1980 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 1980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.