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 420, 772, 547, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 772, 547, 15 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 420, 772, 547, 15 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 420, 772, 547, 15 is 1.
HCF(420, 772, 547, 15) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 772, 547, 15 is 1.
Step 1: Since 772 > 420, we apply the division lemma to 772 and 420, to get
772 = 420 x 1 + 352
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 352 and 420, to get
420 = 352 x 1 + 68
Step 3: We consider the new divisor 352 and the new remainder 68, and apply the division lemma to get
352 = 68 x 5 + 12
We consider the new divisor 68 and the new remainder 12,and apply the division lemma to get
68 = 12 x 5 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 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 420 and 772 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(68,12) = HCF(352,68) = HCF(420,352) = HCF(772,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 547 > 4, we apply the division lemma to 547 and 4, to get
547 = 4 x 136 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 547 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(547,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1
Notice that 1 = HCF(15,1) .
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 420, 772, 547, 15?
Answer: HCF of 420, 772, 547, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 772, 547, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 772, 547, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.