Highest Common Factor of 408, 238, 745 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 408, 238, 745 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 238, 745 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 408, 238, 745 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 408, 238, 745 is 1.
HCF(408, 238, 745) = 1
HCF of 408, 238, 745 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 238, 745 is 1.
Highest Common Factor of 408,238,745 is 1
Step 1: Since 408 > 238, we apply the division lemma to 408 and 238, to get
408 = 238 x 1 + 170
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 170 and 238, to get
238 = 170 x 1 + 68
Step 3: We consider the new divisor 170 and the new remainder 68, and apply the division lemma to get
170 = 68 x 2 + 34
We consider the new divisor 68 and the new remainder 34, and apply the division lemma to get
68 = 34 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 408 and 238 is 34
Notice that 34 = HCF(68,34) = HCF(170,68) = HCF(238,170) = HCF(408,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 745 > 34, we apply the division lemma to 745 and 34, to get
745 = 34 x 21 + 31
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 31 and 34, to get
34 = 31 x 1 + 3
Step 3: We consider the new divisor 31 and the new remainder 3, and apply the division lemma to get
31 = 3 x 10 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 34 and 745 is 1
Notice that 1 = HCF(3,1) = HCF(31,3) = HCF(34,31) = HCF(745,34) .
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Frequently Asked Questions on HCF of 408, 238, 745 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 408, 238, 745?
Answer: HCF of 408, 238, 745 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 238, 745 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 238, 745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.