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 498, 677, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 677, 278 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 498, 677, 278 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 498, 677, 278 is 1.
HCF(498, 677, 278) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 677, 278 is 1.
Step 1: Since 677 > 498, we apply the division lemma to 677 and 498, to get
677 = 498 x 1 + 179
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 179 and 498, to get
498 = 179 x 2 + 140
Step 3: We consider the new divisor 179 and the new remainder 140, and apply the division lemma to get
179 = 140 x 1 + 39
We consider the new divisor 140 and the new remainder 39,and apply the division lemma to get
140 = 39 x 3 + 23
We consider the new divisor 39 and the new remainder 23,and apply the division lemma to get
39 = 23 x 1 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 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 498 and 677 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(39,23) = HCF(140,39) = HCF(179,140) = HCF(498,179) = HCF(677,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 1, we apply the division lemma to 278 and 1, to get
278 = 1 x 278 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 278 is 1
Notice that 1 = HCF(278,1) .
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 498, 677, 278?
Answer: HCF of 498, 677, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 677, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 677, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.