Highest Common Factor of 72, 45, 64, 122 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 72, 45, 64, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 45, 64, 122 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 72, 45, 64, 122 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 72, 45, 64, 122 is 1.
HCF(72, 45, 64, 122) = 1
HCF of 72, 45, 64, 122 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 72, 45, 64, 122 is 1.
Highest Common Factor of 72,45,64,122 is 1
Step 1: Since 72 > 45, we apply the division lemma to 72 and 45, to get
72 = 45 x 1 + 27
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 27 and 45, to get
45 = 27 x 1 + 18
Step 3: We consider the new divisor 27 and the new remainder 18, and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 72 and 45 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) = HCF(72,45) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64 > 9, we apply the division lemma to 64 and 9, to get
64 = 9 x 7 + 1
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 1 and 9, to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 64 is 1
Notice that 1 = HCF(9,1) = HCF(64,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 122 > 1, we apply the division lemma to 122 and 1, to get
122 = 1 x 122 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1
Notice that 1 = HCF(122,1) .
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Frequently Asked Questions on HCF of 72, 45, 64, 122 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 72, 45, 64, 122?
Answer: HCF of 72, 45, 64, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 45, 64, 122 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 45, 64, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.