Highest Common Factor of 45, 60, 120 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 45, 60, 120 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 45, 60, 120 is 15 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 45, 60, 120 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 45, 60, 120 is 15.
HCF(45, 60, 120) = 15
HCF of 45, 60, 120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 45, 60, 120 is 15.
Highest Common Factor of 45,60,120 is 15
Step 1: Since 60 > 45, we apply the division lemma to 60 and 45, to get
60 = 45 x 1 + 15
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 15 and 45, to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 45 and 60 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 15, we apply the division lemma to 120 and 15, to get
120 = 15 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 120 is 15
Notice that 15 = HCF(120,15) .
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Frequently Asked Questions on HCF of 45, 60, 120 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 45, 60, 120?
Answer: HCF of 45, 60, 120 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 45, 60, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 45, 60, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
