Highest Common Factor of 678, 465, 120 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, 465, 120 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 465, 120 is 3 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, 465, 120 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, 465, 120 is 3.
HCF(678, 465, 120) = 3
HCF of 678, 465, 120 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, 465, 120 is 3.
Highest Common Factor of 678,465,120 is 3
Step 1: Since 678 > 465, we apply the division lemma to 678 and 465, to get
678 = 465 x 1 + 213
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 213 and 465, to get
465 = 213 x 2 + 39
Step 3: We consider the new divisor 213 and the new remainder 39, and apply the division lemma to get
213 = 39 x 5 + 18
We consider the new divisor 39 and the new remainder 18,and apply the division lemma to get
39 = 18 x 2 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 465 is 3
Notice that 3 = HCF(18,3) = HCF(39,18) = HCF(213,39) = HCF(465,213) = HCF(678,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 3, we apply the division lemma to 120 and 3, to get
120 = 3 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 120 is 3
Notice that 3 = HCF(120,3) .
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Frequently Asked Questions on HCF of 678, 465, 120 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, 465, 120?
Answer: HCF of 678, 465, 120 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 465, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 465, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.