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 360, 600, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 600, 83 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 360, 600, 83 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 360, 600, 83 is 1.
HCF(360, 600, 83) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 600, 83 is 1.
Step 1: Since 600 > 360, we apply the division lemma to 600 and 360, to get
600 = 360 x 1 + 240
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 240 and 360, to get
360 = 240 x 1 + 120
Step 3: We consider the new divisor 240 and the new remainder 120, and apply the division lemma to get
240 = 120 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 120, the HCF of 360 and 600 is 120
Notice that 120 = HCF(240,120) = HCF(360,240) = HCF(600,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 83, we apply the division lemma to 120 and 83, to get
120 = 83 x 1 + 37
Step 2: Since the reminder 83 ≠ 0, we apply division lemma to 37 and 83, to get
83 = 37 x 2 + 9
Step 3: We consider the new divisor 37 and the new remainder 9, and apply the division lemma to get
37 = 9 x 4 + 1
We consider the new divisor 9 and the new remainder 1, and apply the division lemma 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 120 and 83 is 1
Notice that 1 = HCF(9,1) = HCF(37,9) = HCF(83,37) = HCF(120,83) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 360, 600, 83?
Answer: HCF of 360, 600, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 600, 83 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 600, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.