Highest Common Factor of 270, 780, 880, 675 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 270, 780, 880, 675 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 780, 880, 675 is 5 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 270, 780, 880, 675 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 270, 780, 880, 675 is 5.
HCF(270, 780, 880, 675) = 5
HCF of 270, 780, 880, 675 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 780, 880, 675 is 5.
Highest Common Factor of 270,780,880,675 is 5
Step 1: Since 780 > 270, we apply the division lemma to 780 and 270, to get
780 = 270 x 2 + 240
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 240 and 270, to get
270 = 240 x 1 + 30
Step 3: We consider the new divisor 240 and the new remainder 30, and apply the division lemma to get
240 = 30 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 270 and 780 is 30
Notice that 30 = HCF(240,30) = HCF(270,240) = HCF(780,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 880 > 30, we apply the division lemma to 880 and 30, to get
880 = 30 x 29 + 10
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 10 and 30, to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 30 and 880 is 10
Notice that 10 = HCF(30,10) = HCF(880,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 675 > 10, we apply the division lemma to 675 and 10, to get
675 = 10 x 67 + 5
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 5 and 10, to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 10 and 675 is 5
Notice that 5 = HCF(10,5) = HCF(675,10) .
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Frequently Asked Questions on HCF of 270, 780, 880, 675 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 270, 780, 880, 675?
Answer: HCF of 270, 780, 880, 675 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 780, 880, 675 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 780, 880, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
