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 972, 576, 130 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 576, 130 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 972, 576, 130 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 972, 576, 130 is 2.
HCF(972, 576, 130) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 576, 130 is 2.
Step 1: Since 972 > 576, we apply the division lemma to 972 and 576, to get
972 = 576 x 1 + 396
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 396 and 576, to get
576 = 396 x 1 + 180
Step 3: We consider the new divisor 396 and the new remainder 180, and apply the division lemma to get
396 = 180 x 2 + 36
We consider the new divisor 180 and the new remainder 36, and apply the division lemma to get
180 = 36 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 972 and 576 is 36
Notice that 36 = HCF(180,36) = HCF(396,180) = HCF(576,396) = HCF(972,576) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 130 > 36, we apply the division lemma to 130 and 36, to get
130 = 36 x 3 + 22
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 22 and 36, to get
36 = 22 x 1 + 14
Step 3: We consider the new divisor 22 and the new remainder 14, and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
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 36 and 130 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(130,36) .
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 972, 576, 130?
Answer: HCF of 972, 576, 130 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 576, 130 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 576, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.