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Highest Common Factor of 84, 210, 336 using Euclid's algorithm

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 84, 210, 336 i.e. 42 the largest integer that leaves a remainder zero for all numbers.

HCF of 84, 210, 336 is 42 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 84, 210, 336 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 84, 210, 336 is 42.

HCF(84, 210, 336) = 42

HCF of 84, 210, 336 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 84, 210, 336 is 42.

Highest Common Factor of 84,210,336 using Euclid's algorithm

Step 1: Since 210 > 84, we apply the division lemma to 210 and 84, to get

210 = 84 x 2 + 42

Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 42 and 84, to get

84 = 42 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 84 and 210 is 42

Notice that 42 = HCF(84,42) = HCF(210,84) .


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

Step 1: Since 336 > 42, we apply the division lemma to 336 and 42, to get

336 = 42 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 42 and 336 is 42

Notice that 42 = HCF(336,42) .

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Frequently Asked Questions on HCF of 84, 210, 336 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 84, 210, 336?

Answer: HCF of 84, 210, 336 is 42 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 84, 210, 336 using Euclid's Algorithm?

Answer: For arbitrary numbers 84, 210, 336 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.