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, 910, 769 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 910, 769 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, 910, 769 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, 910, 769 is 1.
HCF(498, 910, 769) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 910, 769 is 1.
Step 1: Since 910 > 498, we apply the division lemma to 910 and 498, to get
910 = 498 x 1 + 412
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 412 and 498, to get
498 = 412 x 1 + 86
Step 3: We consider the new divisor 412 and the new remainder 86, and apply the division lemma to get
412 = 86 x 4 + 68
We consider the new divisor 86 and the new remainder 68,and apply the division lemma to get
86 = 68 x 1 + 18
We consider the new divisor 68 and the new remainder 18,and apply the division lemma to get
68 = 18 x 3 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 498 and 910 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(68,18) = HCF(86,68) = HCF(412,86) = HCF(498,412) = HCF(910,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 769 > 2, we apply the division lemma to 769 and 2, to get
769 = 2 x 384 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 769 is 1
Notice that 1 = HCF(2,1) = HCF(769,2) .
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 498, 910, 769?
Answer: HCF of 498, 910, 769 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 910, 769 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 910, 769 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.