HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 21, 40, 84, 98 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 21, 40, 84, 98 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 21, 40, 84, 98 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 21, 40, 84, 98 is **1**.

HCF(21, 40, 84, 98) = 1

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

Highest common factor (HCF) of 21, 40, 84, 98 is **1**.

**Step 1:** Since 40 > 21, we apply the division lemma to 40 and 21, to get

40 = 21 x 1 + 19

**Step 2:** Since the reminder 21 ≠ 0, we apply division lemma to 19 and 21, to get

21 = 19 x 1 + 2

**Step 3:** We consider the new divisor 19 and the new remainder 2, and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 40 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) .

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

**Step 1:** Since 84 > 1, we apply the division lemma to 84 and 1, to get

84 = 1 x 84 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1

Notice that 1 = HCF(84,1) .

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

**Step 1:** Since 98 > 1, we apply the division lemma to 98 and 1, to get

98 = 1 x 98 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 98 is 1

Notice that 1 = HCF(98,1) .

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 21, 40, 84, 98?

Answer: HCF of 21, 40, 84, 98 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 21, 40, 84, 98 using Euclid's Algorithm?

Answer: For arbitrary numbers 21, 40, 84, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.