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 960, 690, 38 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 690, 38 is 2 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 960, 690, 38 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 960, 690, 38 is 2.
HCF(960, 690, 38) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 960, 690, 38 is 2.
Step 1: Since 960 > 690, we apply the division lemma to 960 and 690, to get
960 = 690 x 1 + 270
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 270 and 690, to get
690 = 270 x 2 + 150
Step 3: We consider the new divisor 270 and the new remainder 150, and apply the division lemma to get
270 = 150 x 1 + 120
We consider the new divisor 150 and the new remainder 120,and apply the division lemma to get
150 = 120 x 1 + 30
We consider the new divisor 120 and the new remainder 30,and apply the division lemma to get
120 = 30 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 960 and 690 is 30
Notice that 30 = HCF(120,30) = HCF(150,120) = HCF(270,150) = HCF(690,270) = HCF(960,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 30, we apply the division lemma to 38 and 30, to get
38 = 30 x 1 + 8
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 8 and 30, to get
30 = 8 x 3 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 30 and 38 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) .
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 960, 690, 38?
Answer: HCF of 960, 690, 38 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 690, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 690, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.