Highest Common Factor of 460, 754, 109 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 460, 754, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 754, 109 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 460, 754, 109 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 460, 754, 109 is 1.
HCF(460, 754, 109) = 1
HCF of 460, 754, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 754, 109 is 1.
Highest Common Factor of 460,754,109 is 1
Step 1: Since 754 > 460, we apply the division lemma to 754 and 460, to get
754 = 460 x 1 + 294
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 294 and 460, to get
460 = 294 x 1 + 166
Step 3: We consider the new divisor 294 and the new remainder 166, and apply the division lemma to get
294 = 166 x 1 + 128
We consider the new divisor 166 and the new remainder 128,and apply the division lemma to get
166 = 128 x 1 + 38
We consider the new divisor 128 and the new remainder 38,and apply the division lemma to get
128 = 38 x 3 + 14
We consider the new divisor 38 and the new remainder 14,and apply the division lemma to get
38 = 14 x 2 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 460 and 754 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(38,14) = HCF(128,38) = HCF(166,128) = HCF(294,166) = HCF(460,294) = HCF(754,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 2, we apply the division lemma to 109 and 2, to get
109 = 2 x 54 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 109 is 1
Notice that 1 = HCF(2,1) = HCF(109,2) .
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Frequently Asked Questions on HCF of 460, 754, 109 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 460, 754, 109?
Answer: HCF of 460, 754, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 754, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 754, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
