Highest Common Factor of 755, 996, 133 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 755, 996, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 755, 996, 133 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 755, 996, 133 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 755, 996, 133 is 1.
HCF(755, 996, 133) = 1
HCF of 755, 996, 133 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 755, 996, 133 is 1.
Highest Common Factor of 755,996,133 is 1
Step 1: Since 996 > 755, we apply the division lemma to 996 and 755, to get
996 = 755 x 1 + 241
Step 2: Since the reminder 755 ≠ 0, we apply division lemma to 241 and 755, to get
755 = 241 x 3 + 32
Step 3: We consider the new divisor 241 and the new remainder 32, and apply the division lemma to get
241 = 32 x 7 + 17
We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get
32 = 17 x 1 + 15
We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get
17 = 15 x 1 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 755 and 996 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(241,32) = HCF(755,241) = HCF(996,755) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 133 > 1, we apply the division lemma to 133 and 1, to get
133 = 1 x 133 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 133 is 1
Notice that 1 = HCF(133,1) .
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Frequently Asked Questions on HCF of 755, 996, 133 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 755, 996, 133?
Answer: HCF of 755, 996, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 755, 996, 133 using Euclid's Algorithm?
Answer: For arbitrary numbers 755, 996, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.