Highest Common Factor of 757, 500 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 757, 500 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 757, 500 is 1 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 757, 500 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 757, 500 is 1.
HCF(757, 500) = 1
HCF of 757, 500 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 757, 500 is 1.
Highest Common Factor of 757,500 is 1
Step 1: Since 757 > 500, we apply the division lemma to 757 and 500, to get
757 = 500 x 1 + 257
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 257 and 500, to get
500 = 257 x 1 + 243
Step 3: We consider the new divisor 257 and the new remainder 243, and apply the division lemma to get
257 = 243 x 1 + 14
We consider the new divisor 243 and the new remainder 14,and apply the division lemma to get
243 = 14 x 17 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 500 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(243,14) = HCF(257,243) = HCF(500,257) = HCF(757,500) .
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Frequently Asked Questions on HCF of 757, 500 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 757, 500?
Answer: HCF of 757, 500 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 757, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 757, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.