Highest Common Factor of 266, 749 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 266, 749 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 266, 749 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 266, 749 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 266, 749 is 7.
HCF(266, 749) = 7
HCF of 266, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 266, 749 is 7.
Highest Common Factor of 266,749 is 7
Step 1: Since 749 > 266, we apply the division lemma to 749 and 266, to get
749 = 266 x 2 + 217
Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 217 and 266, to get
266 = 217 x 1 + 49
Step 3: We consider the new divisor 217 and the new remainder 49, and apply the division lemma to get
217 = 49 x 4 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 266 and 749 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(217,49) = HCF(266,217) = HCF(749,266) .
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Frequently Asked Questions on HCF of 266, 749 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 266, 749?
Answer: HCF of 266, 749 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 266, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 266, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
