Highest Common Factor of 105, 147, 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 105, 147, 189 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 147, 189 is 21 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 105, 147, 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 105, 147, 189 is 21.
HCF(105, 147, 189) = 21
HCF of 105, 147, 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 105, 147, 189 is 21.
Highest Common Factor of 105,147,189 is 21
Step 1: Since 147 > 105, we apply the division lemma to 147 and 105, to get
147 = 105 x 1 + 42
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 42 and 105, to get
105 = 42 x 2 + 21
Step 3: We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 105 and 147 is 21
Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(147,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 189 > 21, we apply the division lemma to 189 and 21, to get
189 = 21 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 21 and 189 is 21
Notice that 21 = HCF(189,21) .
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Frequently Asked Questions on HCF of 105, 147, 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 105, 147, 189?
Answer: HCF of 105, 147, 189 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 147, 189 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 147, 189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
