Highest Common Factor of 760, 308, 709, 450 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 760, 308, 709, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 760, 308, 709, 450 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 760, 308, 709, 450 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 760, 308, 709, 450 is 1.
HCF(760, 308, 709, 450) = 1
HCF of 760, 308, 709, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 760, 308, 709, 450 is 1.
Highest Common Factor of 760,308,709,450 is 1
Step 1: Since 760 > 308, we apply the division lemma to 760 and 308, to get
760 = 308 x 2 + 144
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 144 and 308, to get
308 = 144 x 2 + 20
Step 3: We consider the new divisor 144 and the new remainder 20, and apply the division lemma to get
144 = 20 x 7 + 4
We consider the new divisor 20 and the new remainder 4, and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 760 and 308 is 4
Notice that 4 = HCF(20,4) = HCF(144,20) = HCF(308,144) = HCF(760,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 4, we apply the division lemma to 709 and 4, to get
709 = 4 x 177 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 709 is 1
Notice that 1 = HCF(4,1) = HCF(709,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 1, we apply the division lemma to 450 and 1, to get
450 = 1 x 450 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 450 is 1
Notice that 1 = HCF(450,1) .
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Frequently Asked Questions on HCF of 760, 308, 709, 450 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 760, 308, 709, 450?
Answer: HCF of 760, 308, 709, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 760, 308, 709, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 760, 308, 709, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.