Highest Common Factor of 308, 511 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 308, 511 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 308, 511 is 7 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 308, 511 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 308, 511 is 7.
HCF(308, 511) = 7
HCF of 308, 511 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 308, 511 is 7.
Highest Common Factor of 308,511 is 7
Step 1: Since 511 > 308, we apply the division lemma to 511 and 308, to get
511 = 308 x 1 + 203
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 203 and 308, to get
308 = 203 x 1 + 105
Step 3: We consider the new divisor 203 and the new remainder 105, and apply the division lemma to get
203 = 105 x 1 + 98
We consider the new divisor 105 and the new remainder 98,and apply the division lemma to get
105 = 98 x 1 + 7
We consider the new divisor 98 and the new remainder 7,and apply the division lemma to get
98 = 7 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 308 and 511 is 7
Notice that 7 = HCF(98,7) = HCF(105,98) = HCF(203,105) = HCF(308,203) = HCF(511,308) .
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Frequently Asked Questions on HCF of 308, 511 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 308, 511?
Answer: HCF of 308, 511 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 308, 511 using Euclid's Algorithm?
Answer: For arbitrary numbers 308, 511 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.