Highest Common Factor of 98, 70, 91, 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 98, 70, 91, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 98, 70, 91, 218 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 98, 70, 91, 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 98, 70, 91, 218 is 1.
HCF(98, 70, 91, 218) = 1
HCF of 98, 70, 91, 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 98, 70, 91, 218 is 1.
Highest Common Factor of 98,70,91,218 is 1
Step 1: Since 98 > 70, we apply the division lemma to 98 and 70, to get
98 = 70 x 1 + 28
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 28 and 70, to get
70 = 28 x 2 + 14
Step 3: We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 98 and 70 is 14
Notice that 14 = HCF(28,14) = HCF(70,28) = HCF(98,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 91 > 14, we apply the division lemma to 91 and 14, to get
91 = 14 x 6 + 7
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 14 and 91 is 7
Notice that 7 = HCF(14,7) = HCF(91,14) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 218 > 7, we apply the division lemma to 218 and 7, to get
218 = 7 x 31 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 218 is 1
Notice that 1 = HCF(7,1) = HCF(218,7) .
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Frequently Asked Questions on HCF of 98, 70, 91, 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 98, 70, 91, 218?
Answer: HCF of 98, 70, 91, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 98, 70, 91, 218 using Euclid's Algorithm?
Answer: For arbitrary numbers 98, 70, 91, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.