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 147, 567, 192 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 147, 567, 192 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 147, 567, 192 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 147, 567, 192 is 3.
HCF(147, 567, 192) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 147, 567, 192 is 3.
Step 1: Since 567 > 147, we apply the division lemma to 567 and 147, to get
567 = 147 x 3 + 126
Step 2: Since the reminder 147 ≠ 0, we apply division lemma to 126 and 147, to get
147 = 126 x 1 + 21
Step 3: We consider the new divisor 126 and the new remainder 21, and apply the division lemma to get
126 = 21 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 147 and 567 is 21
Notice that 21 = HCF(126,21) = HCF(147,126) = HCF(567,147) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 192 > 21, we apply the division lemma to 192 and 21, to get
192 = 21 x 9 + 3
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 3 and 21, to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 192 is 3
Notice that 3 = HCF(21,3) = HCF(192,21) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 147, 567, 192?
Answer: HCF of 147, 567, 192 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 147, 567, 192 using Euclid's Algorithm?
Answer: For arbitrary numbers 147, 567, 192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.