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 542, 6860, 4778 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 6860, 4778 is 2 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 542, 6860, 4778 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 542, 6860, 4778 is 2.
HCF(542, 6860, 4778) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 6860, 4778 is 2.
Step 1: Since 6860 > 542, we apply the division lemma to 6860 and 542, to get
6860 = 542 x 12 + 356
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 356 and 542, to get
542 = 356 x 1 + 186
Step 3: We consider the new divisor 356 and the new remainder 186, and apply the division lemma to get
356 = 186 x 1 + 170
We consider the new divisor 186 and the new remainder 170,and apply the division lemma to get
186 = 170 x 1 + 16
We consider the new divisor 170 and the new remainder 16,and apply the division lemma to get
170 = 16 x 10 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 6860 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(170,16) = HCF(186,170) = HCF(356,186) = HCF(542,356) = HCF(6860,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4778 > 2, we apply the division lemma to 4778 and 2, to get
4778 = 2 x 2389 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 4778 is 2
Notice that 2 = HCF(4778,2) .
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 542, 6860, 4778?
Answer: HCF of 542, 6860, 4778 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 6860, 4778 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 6860, 4778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.