Highest Common Factor of 486, 786, 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 486, 786, 120 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 486, 786, 120 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 486, 786, 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 486, 786, 120 is 6.
HCF(486, 786, 120) = 6
HCF of 486, 786, 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 486, 786, 120 is 6.
Highest Common Factor of 486,786,120 is 6
Step 1: Since 786 > 486, we apply the division lemma to 786 and 486, to get
786 = 486 x 1 + 300
Step 2: Since the reminder 486 ≠ 0, we apply division lemma to 300 and 486, to get
486 = 300 x 1 + 186
Step 3: We consider the new divisor 300 and the new remainder 186, and apply the division lemma to get
300 = 186 x 1 + 114
We consider the new divisor 186 and the new remainder 114,and apply the division lemma to get
186 = 114 x 1 + 72
We consider the new divisor 114 and the new remainder 72,and apply the division lemma to get
114 = 72 x 1 + 42
We consider the new divisor 72 and the new remainder 42,and apply the division lemma to get
72 = 42 x 1 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 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 486 and 786 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(72,42) = HCF(114,72) = HCF(186,114) = HCF(300,186) = HCF(486,300) = HCF(786,486) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 6, we apply the division lemma to 120 and 6, to get
120 = 6 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 120 is 6
Notice that 6 = HCF(120,6) .
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Frequently Asked Questions on HCF of 486, 786, 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 486, 786, 120?
Answer: HCF of 486, 786, 120 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 486, 786, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 486, 786, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.