Highest Common Factor of 510, 800, 972 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 510, 800, 972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 800, 972 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 510, 800, 972 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 510, 800, 972 is 2.
HCF(510, 800, 972) = 2
HCF of 510, 800, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 800, 972 is 2.
Highest Common Factor of 510,800,972 is 2
Step 1: Since 800 > 510, we apply the division lemma to 800 and 510, to get
800 = 510 x 1 + 290
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 290 and 510, to get
510 = 290 x 1 + 220
Step 3: We consider the new divisor 290 and the new remainder 220, and apply the division lemma to get
290 = 220 x 1 + 70
We consider the new divisor 220 and the new remainder 70,and apply the division lemma to get
220 = 70 x 3 + 10
We consider the new divisor 70 and the new remainder 10,and apply the division lemma to get
70 = 10 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 510 and 800 is 10
Notice that 10 = HCF(70,10) = HCF(220,70) = HCF(290,220) = HCF(510,290) = HCF(800,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 10, we apply the division lemma to 972 and 10, to get
972 = 10 x 97 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 972 is 2
Notice that 2 = HCF(10,2) = HCF(972,10) .
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Frequently Asked Questions on HCF of 510, 800, 972 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 510, 800, 972?
Answer: HCF of 510, 800, 972 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 800, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 800, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.