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 192, 690, 30 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 192, 690, 30 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 192, 690, 30 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 192, 690, 30 is 6.
HCF(192, 690, 30) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 192, 690, 30 is 6.
Step 1: Since 690 > 192, we apply the division lemma to 690 and 192, to get
690 = 192 x 3 + 114
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 114 and 192, to get
192 = 114 x 1 + 78
Step 3: We consider the new divisor 114 and the new remainder 78, and apply the division lemma to get
114 = 78 x 1 + 36
We consider the new divisor 78 and the new remainder 36,and apply the division lemma to get
78 = 36 x 2 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 192 and 690 is 6
Notice that 6 = HCF(36,6) = HCF(78,36) = HCF(114,78) = HCF(192,114) = HCF(690,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 6, we apply the division lemma to 30 and 6, to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 30 is 6
Notice that 6 = HCF(30,6) .
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 192, 690, 30?
Answer: HCF of 192, 690, 30 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 192, 690, 30 using Euclid's Algorithm?
Answer: For arbitrary numbers 192, 690, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.