Highest Common Factor of 750, 980, 218 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 750, 980, 218 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 980, 218 is 2 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 750, 980, 218 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 750, 980, 218 is 2.
HCF(750, 980, 218) = 2
HCF of 750, 980, 218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 750, 980, 218 is 2.
Highest Common Factor of 750,980,218 is 2
Step 1: Since 980 > 750, we apply the division lemma to 980 and 750, to get
980 = 750 x 1 + 230
Step 2: Since the reminder 750 ≠ 0, we apply division lemma to 230 and 750, to get
750 = 230 x 3 + 60
Step 3: We consider the new divisor 230 and the new remainder 60, and apply the division lemma to get
230 = 60 x 3 + 50
We consider the new divisor 60 and the new remainder 50,and apply the division lemma to get
60 = 50 x 1 + 10
We consider the new divisor 50 and the new remainder 10,and apply the division lemma to get
50 = 10 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 750 and 980 is 10
Notice that 10 = HCF(50,10) = HCF(60,50) = HCF(230,60) = HCF(750,230) = HCF(980,750) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 218 > 10, we apply the division lemma to 218 and 10, to get
218 = 10 x 21 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 218 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(218,10) .
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Frequently Asked Questions on HCF of 750, 980, 218 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 750, 980, 218?
Answer: HCF of 750, 980, 218 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 980, 218 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 980, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.