Highest Common Factor of 6272, 304 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 6272, 304 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 6272, 304 is 16 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 6272, 304 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 6272, 304 is 16.
HCF(6272, 304) = 16
HCF of 6272, 304 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6272, 304 is 16.
Highest Common Factor of 6272,304 is 16
Step 1: Since 6272 > 304, we apply the division lemma to 6272 and 304, to get
6272 = 304 x 20 + 192
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 192 and 304, to get
304 = 192 x 1 + 112
Step 3: We consider the new divisor 192 and the new remainder 112, and apply the division lemma to get
192 = 112 x 1 + 80
We consider the new divisor 112 and the new remainder 80,and apply the division lemma to get
112 = 80 x 1 + 32
We consider the new divisor 80 and the new remainder 32,and apply the division lemma to get
80 = 32 x 2 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 6272 and 304 is 16
Notice that 16 = HCF(32,16) = HCF(80,32) = HCF(112,80) = HCF(192,112) = HCF(304,192) = HCF(6272,304) .
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Frequently Asked Questions on HCF of 6272, 304 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 6272, 304?
Answer: HCF of 6272, 304 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6272, 304 using Euclid's Algorithm?
Answer: For arbitrary numbers 6272, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.