Highest Common Factor of 975, 174, 803 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 975, 174, 803 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 174, 803 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 975, 174, 803 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 975, 174, 803 is 1.
HCF(975, 174, 803) = 1
HCF of 975, 174, 803 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 174, 803 is 1.
Highest Common Factor of 975,174,803 is 1
Step 1: Since 975 > 174, we apply the division lemma to 975 and 174, to get
975 = 174 x 5 + 105
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 105 and 174, to get
174 = 105 x 1 + 69
Step 3: We consider the new divisor 105 and the new remainder 69, and apply the division lemma to get
105 = 69 x 1 + 36
We consider the new divisor 69 and the new remainder 36,and apply the division lemma to get
69 = 36 x 1 + 33
We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get
36 = 33 x 1 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 975 and 174 is 3
Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(69,36) = HCF(105,69) = HCF(174,105) = HCF(975,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 803 > 3, we apply the division lemma to 803 and 3, to get
803 = 3 x 267 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 803 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(803,3) .
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Frequently Asked Questions on HCF of 975, 174, 803 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 975, 174, 803?
Answer: HCF of 975, 174, 803 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 174, 803 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 174, 803 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.