Highest Common Factor of 96, 336, 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 96, 336, 189 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 96, 336, 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 96, 336, 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 96, 336, 189 is 3.
HCF(96, 336, 189) = 3
HCF of 96, 336, 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 96, 336, 189 is 3.
Highest Common Factor of 96,336,189 is 3
Step 1: Since 336 > 96, we apply the division lemma to 336 and 96, to get
336 = 96 x 3 + 48
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 48 and 96, to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 96 and 336 is 48
Notice that 48 = HCF(96,48) = HCF(336,96) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 189 > 48, we apply the division lemma to 189 and 48, to get
189 = 48 x 3 + 45
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 45 and 48, to get
48 = 45 x 1 + 3
Step 3: We consider the new divisor 45 and the new remainder 3, and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 48 and 189 is 3
Notice that 3 = HCF(45,3) = HCF(48,45) = HCF(189,48) .
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Frequently Asked Questions on HCF of 96, 336, 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 96, 336, 189?
Answer: HCF of 96, 336, 189 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 96, 336, 189 using Euclid's Algorithm?
Answer: For arbitrary numbers 96, 336, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.