Highest Common Factor of 336, 777 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 336, 777 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 777 is 21 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 336, 777 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 336, 777 is 21.
HCF(336, 777) = 21
HCF of 336, 777 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 777 is 21.
Highest Common Factor of 336,777 is 21
Step 1: Since 777 > 336, we apply the division lemma to 777 and 336, to get
777 = 336 x 2 + 105
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 105 and 336, to get
336 = 105 x 3 + 21
Step 3: We consider the new divisor 105 and the new remainder 21, and apply the division lemma to get
105 = 21 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 336 and 777 is 21
Notice that 21 = HCF(105,21) = HCF(336,105) = HCF(777,336) .
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Frequently Asked Questions on HCF of 336, 777 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 336, 777?
Answer: HCF of 336, 777 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 777 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.