Highest Common Factor of 648, 761, 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 648, 761, 120 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 761, 120 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 648, 761, 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 648, 761, 120 is 1.
HCF(648, 761, 120) = 1
HCF of 648, 761, 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 648, 761, 120 is 1.
Highest Common Factor of 648,761,120 is 1
Step 1: Since 761 > 648, we apply the division lemma to 761 and 648, to get
761 = 648 x 1 + 113
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 113 and 648, to get
648 = 113 x 5 + 83
Step 3: We consider the new divisor 113 and the new remainder 83, and apply the division lemma to get
113 = 83 x 1 + 30
We consider the new divisor 83 and the new remainder 30,and apply the division lemma to get
83 = 30 x 2 + 23
We consider the new divisor 30 and the new remainder 23,and apply the division lemma to get
30 = 23 x 1 + 7
We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get
23 = 7 x 3 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 648 and 761 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(83,30) = HCF(113,83) = HCF(648,113) = HCF(761,648) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 1, we apply the division lemma to 120 and 1, to get
120 = 1 x 120 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 120 is 1
Notice that 1 = HCF(120,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 648, 761, 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 648, 761, 120?
Answer: HCF of 648, 761, 120 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 761, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 761, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.