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, 960, 692, 813 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 960, 692, 813 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, 960, 692, 813 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, 960, 692, 813 is 1.
HCF(360, 960, 692, 813) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 960, 692, 813 is 1.
Step 1: Since 960 > 360, we apply the division lemma to 960 and 360, to get
960 = 360 x 2 + 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 960 is 120
Notice that 120 = HCF(240,120) = HCF(360,240) = HCF(960,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 692 > 120, we apply the division lemma to 692 and 120, to get
692 = 120 x 5 + 92
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 92 and 120, to get
120 = 92 x 1 + 28
Step 3: We consider the new divisor 92 and the new remainder 28, and apply the division lemma to get
92 = 28 x 3 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 120 and 692 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(92,28) = HCF(120,92) = HCF(692,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 813 > 4, we apply the division lemma to 813 and 4, to get
813 = 4 x 203 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 813 is 1
Notice that 1 = HCF(4,1) = HCF(813,4) .
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, 960, 692, 813?
Answer: HCF of 360, 960, 692, 813 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 960, 692, 813 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 960, 692, 813 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.