Highest Common Factor of 258, 400, 749 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 258, 400, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 258, 400, 749 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 258, 400, 749 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 258, 400, 749 is 1.
HCF(258, 400, 749) = 1
HCF of 258, 400, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 258, 400, 749 is 1.
Highest Common Factor of 258,400,749 is 1
Step 1: Since 400 > 258, we apply the division lemma to 400 and 258, to get
400 = 258 x 1 + 142
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 142 and 258, to get
258 = 142 x 1 + 116
Step 3: We consider the new divisor 142 and the new remainder 116, and apply the division lemma to get
142 = 116 x 1 + 26
We consider the new divisor 116 and the new remainder 26,and apply the division lemma to get
116 = 26 x 4 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 258 and 400 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(116,26) = HCF(142,116) = HCF(258,142) = HCF(400,258) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 2, we apply the division lemma to 749 and 2, to get
749 = 2 x 374 + 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 749 is 1
Notice that 1 = HCF(2,1) = HCF(749,2) .
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Frequently Asked Questions on HCF of 258, 400, 749 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 258, 400, 749?
Answer: HCF of 258, 400, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 258, 400, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 258, 400, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.