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, 852, 788 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 852, 788 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 498, 852, 788 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, 852, 788 is 2.
HCF(498, 852, 788) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 852, 788 is 2.
Step 1: Since 852 > 498, we apply the division lemma to 852 and 498, to get
852 = 498 x 1 + 354
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 354 and 498, to get
498 = 354 x 1 + 144
Step 3: We consider the new divisor 354 and the new remainder 144, and apply the division lemma to get
354 = 144 x 2 + 66
We consider the new divisor 144 and the new remainder 66,and apply the division lemma to get
144 = 66 x 2 + 12
We consider the new divisor 66 and the new remainder 12,and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 498 and 852 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(144,66) = HCF(354,144) = HCF(498,354) = HCF(852,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 788 > 6, we apply the division lemma to 788 and 6, to get
788 = 6 x 131 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 788 is 2
Notice that 2 = HCF(6,2) = HCF(788,6) .
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, 852, 788?
Answer: HCF of 498, 852, 788 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 852, 788 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 852, 788 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.