Highest Common Factor of 405, 759, 370 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 405, 759, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 759, 370 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 405, 759, 370 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 405, 759, 370 is 1.
HCF(405, 759, 370) = 1
HCF of 405, 759, 370 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 759, 370 is 1.
Highest Common Factor of 405,759,370 is 1
Step 1: Since 759 > 405, we apply the division lemma to 759 and 405, to get
759 = 405 x 1 + 354
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 354 and 405, to get
405 = 354 x 1 + 51
Step 3: We consider the new divisor 354 and the new remainder 51, and apply the division lemma to get
354 = 51 x 6 + 48
We consider the new divisor 51 and the new remainder 48,and apply the division lemma to get
51 = 48 x 1 + 3
We consider the new divisor 48 and the new remainder 3,and apply the division lemma to get
48 = 3 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 405 and 759 is 3
Notice that 3 = HCF(48,3) = HCF(51,48) = HCF(354,51) = HCF(405,354) = HCF(759,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 3, we apply the division lemma to 370 and 3, to get
370 = 3 x 123 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 370 is 1
Notice that 1 = HCF(3,1) = HCF(370,3) .
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Frequently Asked Questions on HCF of 405, 759, 370 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 405, 759, 370?
Answer: HCF of 405, 759, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 759, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 759, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.