Highest Common Factor of 6276, 9648, 42508 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 6276, 9648, 42508 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 6276, 9648, 42508 is 4 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 6276, 9648, 42508 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 6276, 9648, 42508 is 4.
HCF(6276, 9648, 42508) = 4
HCF of 6276, 9648, 42508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6276, 9648, 42508 is 4.
Highest Common Factor of 6276,9648,42508 is 4
Step 1: Since 9648 > 6276, we apply the division lemma to 9648 and 6276, to get
9648 = 6276 x 1 + 3372
Step 2: Since the reminder 6276 ≠ 0, we apply division lemma to 3372 and 6276, to get
6276 = 3372 x 1 + 2904
Step 3: We consider the new divisor 3372 and the new remainder 2904, and apply the division lemma to get
3372 = 2904 x 1 + 468
We consider the new divisor 2904 and the new remainder 468,and apply the division lemma to get
2904 = 468 x 6 + 96
We consider the new divisor 468 and the new remainder 96,and apply the division lemma to get
468 = 96 x 4 + 84
We consider the new divisor 96 and the new remainder 84,and apply the division lemma to get
96 = 84 x 1 + 12
We consider the new divisor 84 and the new remainder 12,and apply the division lemma to get
84 = 12 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 6276 and 9648 is 12
Notice that 12 = HCF(84,12) = HCF(96,84) = HCF(468,96) = HCF(2904,468) = HCF(3372,2904) = HCF(6276,3372) = HCF(9648,6276) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42508 > 12, we apply the division lemma to 42508 and 12, to get
42508 = 12 x 3542 + 4
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 4 and 12, to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 42508 is 4
Notice that 4 = HCF(12,4) = HCF(42508,12) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6276, 9648, 42508 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 6276, 9648, 42508?
Answer: HCF of 6276, 9648, 42508 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6276, 9648, 42508 using Euclid's Algorithm?
Answer: For arbitrary numbers 6276, 9648, 42508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.