Highest Common Factor of 209, 749, 975 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 209, 749, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 749, 975 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 209, 749, 975 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 209, 749, 975 is 1.
HCF(209, 749, 975) = 1
HCF of 209, 749, 975 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 749, 975 is 1.
Highest Common Factor of 209,749,975 is 1
Step 1: Since 749 > 209, we apply the division lemma to 749 and 209, to get
749 = 209 x 3 + 122
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 122 and 209, to get
209 = 122 x 1 + 87
Step 3: We consider the new divisor 122 and the new remainder 87, and apply the division lemma to get
122 = 87 x 1 + 35
We consider the new divisor 87 and the new remainder 35,and apply the division lemma to get
87 = 35 x 2 + 17
We consider the new divisor 35 and the new remainder 17,and apply the division lemma to get
35 = 17 x 2 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 209 and 749 is 1
Notice that 1 = HCF(17,1) = HCF(35,17) = HCF(87,35) = HCF(122,87) = HCF(209,122) = HCF(749,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 1, we apply the division lemma to 975 and 1, to get
975 = 1 x 975 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 975 is 1
Notice that 1 = HCF(975,1) .
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Frequently Asked Questions on HCF of 209, 749, 975 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 209, 749, 975?
Answer: HCF of 209, 749, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 749, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 749, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.