Highest Common Factor of 778, 498, 46, 522 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 778, 498, 46, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 498, 46, 522 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 778, 498, 46, 522 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 778, 498, 46, 522 is 2.
HCF(778, 498, 46, 522) = 2
HCF of 778, 498, 46, 522 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 498, 46, 522 is 2.
Highest Common Factor of 778,498,46,522 is 2
Step 1: Since 778 > 498, we apply the division lemma to 778 and 498, to get
778 = 498 x 1 + 280
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 280 and 498, to get
498 = 280 x 1 + 218
Step 3: We consider the new divisor 280 and the new remainder 218, and apply the division lemma to get
280 = 218 x 1 + 62
We consider the new divisor 218 and the new remainder 62,and apply the division lemma to get
218 = 62 x 3 + 32
We consider the new divisor 62 and the new remainder 32,and apply the division lemma to get
62 = 32 x 1 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 778 and 498 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(62,32) = HCF(218,62) = HCF(280,218) = HCF(498,280) = HCF(778,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46 > 2, we apply the division lemma to 46 and 2, to get
46 = 2 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 46 is 2
Notice that 2 = HCF(46,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 522 > 2, we apply the division lemma to 522 and 2, to get
522 = 2 x 261 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 522 is 2
Notice that 2 = HCF(522,2) .
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Frequently Asked Questions on HCF of 778, 498, 46, 522 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 778, 498, 46, 522?
Answer: HCF of 778, 498, 46, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 498, 46, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 498, 46, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.