Highest Common Factor of 110, 145, 722, 28 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 110, 145, 722, 28 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 110, 145, 722, 28 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 110, 145, 722, 28 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 110, 145, 722, 28 is 1.
HCF(110, 145, 722, 28) = 1
HCF of 110, 145, 722, 28 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 110, 145, 722, 28 is 1.
Highest Common Factor of 110,145,722,28 is 1
Step 1: Since 145 > 110, we apply the division lemma to 145 and 110, to get
145 = 110 x 1 + 35
Step 2: Since the reminder 110 ≠ 0, we apply division lemma to 35 and 110, to get
110 = 35 x 3 + 5
Step 3: We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 110 and 145 is 5
Notice that 5 = HCF(35,5) = HCF(110,35) = HCF(145,110) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 722 > 5, we apply the division lemma to 722 and 5, to get
722 = 5 x 144 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 722 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(722,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 28 > 1, we apply the division lemma to 28 and 1, to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 28 is 1
Notice that 1 = HCF(28,1) .
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Frequently Asked Questions on HCF of 110, 145, 722, 28 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 110, 145, 722, 28?
Answer: HCF of 110, 145, 722, 28 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 110, 145, 722, 28 using Euclid's Algorithm?
Answer: For arbitrary numbers 110, 145, 722, 28 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.