Highest Common Factor of 498, 676, 978, 802 using Euclid's algorithm
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, 676, 978, 802 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 676, 978, 802 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, 676, 978, 802 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, 676, 978, 802 is 2.
HCF(498, 676, 978, 802) = 2
HCF of 498, 676, 978, 802 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 676, 978, 802 is 2.
Highest Common Factor of 498,676,978,802 is 2
Step 1: Since 676 > 498, we apply the division lemma to 676 and 498, to get
676 = 498 x 1 + 178
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 178 and 498, to get
498 = 178 x 2 + 142
Step 3: We consider the new divisor 178 and the new remainder 142, and apply the division lemma to get
178 = 142 x 1 + 36
We consider the new divisor 142 and the new remainder 36,and apply the division lemma to get
142 = 36 x 3 + 34
We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 498 and 676 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(142,36) = HCF(178,142) = HCF(498,178) = HCF(676,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 2, we apply the division lemma to 978 and 2, to get
978 = 2 x 489 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 978 is 2
Notice that 2 = HCF(978,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 802 > 2, we apply the division lemma to 802 and 2, to get
802 = 2 x 401 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 802 is 2
Notice that 2 = HCF(802,2) .
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Frequently Asked Questions on HCF of 498, 676, 978, 802 using Euclid's Algorithm
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, 676, 978, 802?
Answer: HCF of 498, 676, 978, 802 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 676, 978, 802 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 676, 978, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
