# Highest Common Factor of 30, 42, 77, 30 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 30, 42, 77, 30 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 30, 42, 77, 30 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 30, 42, 77, 30 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 30, 42, 77, 30 is 1.

HCF(30, 42, 77, 30) = 1

## HCF of 30, 42, 77, 30 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 30, 42, 77, 30 is 1. ### Highest Common Factor of 30,42,77,30 is 1

Step 1: Since 42 > 30, we apply the division lemma to 42 and 30, to get

42 = 30 x 1 + 12

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 12 and 30, to get

30 = 12 x 2 + 6

Step 3: 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 30 and 42 is 6

Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) .

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

Step 1: Since 77 > 6, we apply the division lemma to 77 and 6, to get

77 = 6 x 12 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: 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 6 and 77 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(77,6) .

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

Step 1: Since 30 > 1, we apply the division lemma to 30 and 1, to get

30 = 1 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30 is 1

Notice that 1 = HCF(30,1) .

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### Frequently Asked Questions on HCF of 30, 42, 77, 30 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 30, 42, 77, 30?

Answer: HCF of 30, 42, 77, 30 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 30, 42, 77, 30 using Euclid's Algorithm?

Answer: For arbitrary numbers 30, 42, 77, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.