Highest Common Factor of 800, 920, 130 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 800, 920, 130 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 920, 130 is 10 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 800, 920, 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 800, 920, 130 is 10.
HCF(800, 920, 130) = 10
HCF of 800, 920, 130 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 920, 130 is 10.
Highest Common Factor of 800,920,130 is 10
Step 1: Since 920 > 800, we apply the division lemma to 920 and 800, to get
920 = 800 x 1 + 120
Step 2: Since the reminder 800 ≠ 0, we apply division lemma to 120 and 800, to get
800 = 120 x 6 + 80
Step 3: We consider the new divisor 120 and the new remainder 80, and apply the division lemma to get
120 = 80 x 1 + 40
We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 800 and 920 is 40
Notice that 40 = HCF(80,40) = HCF(120,80) = HCF(800,120) = HCF(920,800) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 130 > 40, we apply the division lemma to 130 and 40, to get
130 = 40 x 3 + 10
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 10 and 40, to get
40 = 10 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 40 and 130 is 10
Notice that 10 = HCF(40,10) = HCF(130,40) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 800, 920, 130 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 800, 920, 130?
Answer: HCF of 800, 920, 130 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 920, 130 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 920, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
