Highest Common Factor of 789, 312, 189 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 789, 312, 189 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 789, 312, 189 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 789, 312, 189 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 789, 312, 189 is 3.
HCF(789, 312, 189) = 3
HCF of 789, 312, 189 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 789, 312, 189 is 3.
Highest Common Factor of 789,312,189 is 3
Step 1: Since 789 > 312, we apply the division lemma to 789 and 312, to get
789 = 312 x 2 + 165
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 165 and 312, to get
312 = 165 x 1 + 147
Step 3: We consider the new divisor 165 and the new remainder 147, and apply the division lemma to get
165 = 147 x 1 + 18
We consider the new divisor 147 and the new remainder 18,and apply the division lemma to get
147 = 18 x 8 + 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 789 and 312 is 3
Notice that 3 = HCF(18,3) = HCF(147,18) = HCF(165,147) = HCF(312,165) = HCF(789,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 189 > 3, we apply the division lemma to 189 and 3, to get
189 = 3 x 63 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 189 is 3
Notice that 3 = HCF(189,3) .
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Frequently Asked Questions on HCF of 789, 312, 189 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 789, 312, 189?
Answer: HCF of 789, 312, 189 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 789, 312, 189 using Euclid's Algorithm?
Answer: For arbitrary numbers 789, 312, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.