Highest Common Factor of 165, 440, 98 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 165, 440, 98 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 165, 440, 98 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 165, 440, 98 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 165, 440, 98 is 1.
HCF(165, 440, 98) = 1
HCF of 165, 440, 98 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 165, 440, 98 is 1.
Highest Common Factor of 165,440,98 is 1
Step 1: Since 440 > 165, we apply the division lemma to 440 and 165, to get
440 = 165 x 2 + 110
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 110 and 165, to get
165 = 110 x 1 + 55
Step 3: We consider the new divisor 110 and the new remainder 55, and apply the division lemma to get
110 = 55 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 165 and 440 is 55
Notice that 55 = HCF(110,55) = HCF(165,110) = HCF(440,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 98 > 55, we apply the division lemma to 98 and 55, to get
98 = 55 x 1 + 43
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 43 and 55, to get
55 = 43 x 1 + 12
Step 3: We consider the new divisor 43 and the new remainder 12, and apply the division lemma to get
43 = 12 x 3 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 55 and 98 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(55,43) = HCF(98,55) .
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Frequently Asked Questions on HCF of 165, 440, 98 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 165, 440, 98?
Answer: HCF of 165, 440, 98 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 165, 440, 98 using Euclid's Algorithm?
Answer: For arbitrary numbers 165, 440, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.