Highest Common Factor of 416, 754, 385, 902 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 416, 754, 385, 902 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 416, 754, 385, 902 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 416, 754, 385, 902 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 416, 754, 385, 902 is 1.

HCF(416, 754, 385, 902) = 1

HCF of 416, 754, 385, 902 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 416, 754, 385, 902 is 1.

Highest Common Factor of 416,754,385,902 using Euclid's algorithm

Highest Common Factor of 416,754,385,902 is 1

Step 1: Since 754 > 416, we apply the division lemma to 754 and 416, to get

754 = 416 x 1 + 338

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 338 and 416, to get

416 = 338 x 1 + 78

Step 3: We consider the new divisor 338 and the new remainder 78, and apply the division lemma to get

338 = 78 x 4 + 26

We consider the new divisor 78 and the new remainder 26, and apply the division lemma to get

78 = 26 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 416 and 754 is 26

Notice that 26 = HCF(78,26) = HCF(338,78) = HCF(416,338) = HCF(754,416) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 385 > 26, we apply the division lemma to 385 and 26, to get

385 = 26 x 14 + 21

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 21 and 26, to get

26 = 21 x 1 + 5

Step 3: We consider the new divisor 21 and the new remainder 5, and apply the division lemma to get

21 = 5 x 4 + 1

We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 26 and 385 is 1

Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(26,21) = HCF(385,26) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 902 > 1, we apply the division lemma to 902 and 1, to get

902 = 1 x 902 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 902 is 1

Notice that 1 = HCF(902,1) .

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Frequently Asked Questions on HCF of 416, 754, 385, 902 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 416, 754, 385, 902?

Answer: HCF of 416, 754, 385, 902 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 416, 754, 385, 902 using Euclid's Algorithm?

Answer: For arbitrary numbers 416, 754, 385, 902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.