Highest Common Factor of 321, 749, 102 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 321, 749, 102 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 321, 749, 102 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 321, 749, 102 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 321, 749, 102 is 1.
HCF(321, 749, 102) = 1
HCF of 321, 749, 102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 321, 749, 102 is 1.
Highest Common Factor of 321,749,102 is 1
Step 1: Since 749 > 321, we apply the division lemma to 749 and 321, to get
749 = 321 x 2 + 107
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 107 and 321, to get
321 = 107 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 107, the HCF of 321 and 749 is 107
Notice that 107 = HCF(321,107) = HCF(749,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 102, we apply the division lemma to 107 and 102, to get
107 = 102 x 1 + 5
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 5 and 102, to get
102 = 5 x 20 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 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 107 and 102 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(102,5) = HCF(107,102) .
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Frequently Asked Questions on HCF of 321, 749, 102 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 321, 749, 102?
Answer: HCF of 321, 749, 102 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 321, 749, 102 using Euclid's Algorithm?
Answer: For arbitrary numbers 321, 749, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.