Highest Common Factor of 757, 3577, 5740 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, 3577, 5740 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 757, 3577, 5740 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, 3577, 5740 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, 3577, 5740 is 1.
HCF(757, 3577, 5740) = 1
HCF of 757, 3577, 5740 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, 3577, 5740 is 1.
Highest Common Factor of 757,3577,5740 is 1
Step 1: Since 3577 > 757, we apply the division lemma to 3577 and 757, to get
3577 = 757 x 4 + 549
Step 2: Since the reminder 757 ≠ 0, we apply division lemma to 549 and 757, to get
757 = 549 x 1 + 208
Step 3: We consider the new divisor 549 and the new remainder 208, and apply the division lemma to get
549 = 208 x 2 + 133
We consider the new divisor 208 and the new remainder 133,and apply the division lemma to get
208 = 133 x 1 + 75
We consider the new divisor 133 and the new remainder 75,and apply the division lemma to get
133 = 75 x 1 + 58
We consider the new divisor 75 and the new remainder 58,and apply the division lemma to get
75 = 58 x 1 + 17
We consider the new divisor 58 and the new remainder 17,and apply the division lemma to get
58 = 17 x 3 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 3577 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(58,17) = HCF(75,58) = HCF(133,75) = HCF(208,133) = HCF(549,208) = HCF(757,549) = HCF(3577,757) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5740 > 1, we apply the division lemma to 5740 and 1, to get
5740 = 1 x 5740 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5740 is 1
Notice that 1 = HCF(5740,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 757, 3577, 5740 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, 3577, 5740?
Answer: HCF of 757, 3577, 5740 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 757, 3577, 5740 using Euclid's Algorithm?
Answer: For arbitrary numbers 757, 3577, 5740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
